Finite Group Databasebeta

← C2×#11755186 #14481772

Subgroups — C2×#11755186 #14481772

Order 1920.

2160 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91835C211yesmaximal, characteristic
2C2×C5×#944C211yesmaximal, characteristic, complemented
3C2×C3×#4090C211yesmaximal, characteristic, complemented
4#11755186C2116yesmaximal, direct product factor
5C2×#91424C211yesmaximal, characteristic
6C2×#91411C211yesmaximal, characteristic
7C2×#91404C211yesmaximal, characteristic
8C2×#91403C211yesmaximal, characteristic
9C2×#91402C211yesmaximal, characteristic
10C2×#91379C211yesmaximal, characteristic, complemented
11C2×#91378C211yesmaximal, characteristic, complemented
12C2×#91377C211yesmaximal, characteristic
13C2×#91343C211yesmaximal, characteristic, complemented
14C2×#91334C211yesmaximal, characteristic, complemented
15C2×#91329C211yesmaximal, characteristic, complemented
16C2×#91327C211yesmaximal, characteristic, complemented
17C2×#66063—31nomaximal, Hall
18C22×C3×C5×Q8C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×C5×Dic6C2211yescharacteristic
21C22×C3×Dic10C2211yescharacteristic
22C22×#1204C2211yescharacteristic
23C22×#1200C2211yescharacteristic
24C22×#1200C2211yescharacteristic
25#91835C2218yes—
26C2×#6714C2211yescharacteristic
27C2×#6714C2211yescharacteristic
28C2×C4⋊Dic15C2211yescharacteristic
29C2×#6712C2211yescharacteristic
30C2×#6712C2211yescharacteristic
31C5×#944C2218yescomplemented
32C2×C5×Dic3⋊C4C2211yescharacteristic
33C2×C5×Dic3⋊C4C2211yescharacteristic
34C2×C5×Dic3⋊C4C2211yescharacteristic
35C2×C5×Dic3⋊C4C2211yescharacteristic
36C2×C4×C5×Dic3C2211yescharacteristic
37C3×#4090C2218yescomplemented
38C2×C3×#683C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×C3×#683C2211yescharacteristic
42C2×C3×C4×Dic5C2211yescharacteristic
43C2×Dic3⋊Dic5C2211yescharacteristic
44C2×Dic3⋊Dic5C2211yescharacteristic
45C2×Dic3⋊Dic5C2211yescharacteristic
46C2×#6669C2211yescharacteristic
47C2×#6669C2211yescharacteristic
48C2×#6669C2211yescharacteristic
49C2×#6668C2211yescharacteristic
50C2×#6668C2211yescharacteristic
51C2×#6668C2211yescharacteristic
52C2×#6667C2211yescharacteristic
53C2×#6667C2211yescharacteristic
54C2×Dic3×Dic5C2211yescharacteristic
55C2×Dic3×Dic5C2211yescharacteristic
56#91424C2218yes—
57#91411C2218yes—
58#91404C2218yes—
59#91403C2218yes—
60#91402C2218yes—
61#91379C2218yescomplemented
62#91378C2218yescomplemented
63#91377C2218yes—
64#91343C2218yescomplemented
65#91334C2218yescomplemented
66#91329C2218yescomplemented
67#91327C2218yescomplemented
68C2×#5729—51nomaximal, Hall
69C2×C5×C4⋊Q8—31no—
70C2×#4092—31no—
71C2×#4092—31no—
72C2×#4090—31no—
73C2×#4090D311yescharacteristic, complemented
74#66063—316no—
75C2×#4042—31no—
76C2×#4042—31no—
77C2×#4038—31no—
78C2×D5×C4⋊C4—31no—
79C2×#4036—31no—
80C2×#4035—31no—
81C2×#4035—31no—
82C2×#4034—31no—
83C2×#4018—31no—
84C2×#4016—31no—
85C23×D15C2311yescharacteristic
86C2×C3×C5×Q8—42no—
87C2×C3×C5×Q8C2314yes—
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C2×C4×D15—42no—
95C2×C4×D15C2314yes—
96C22×C5×Dic3C2311yescharacteristic
97C22×C5×Dic3C2311yescharacteristic
98C22×C5×Dic3C2311yescharacteristic
99C22×C5×Dic3C2311yescharacteristic
100C2×C5×Dic6—42no—
101C2×C5×Dic6C2314yes—
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C2×C3×Dic10—42no—
107C2×C3×Dic10C2314yes—
108C2×#1204—42no—
109C2×#1204C2314yes—
110C2×#1200—42no—
111C2×#1200Q818yescomplemented
112C2×#1200C2314yes—
113C2×#1200C2314yes—
114#6714C2314yes—
115#6714C2314yes—
116C4⋊Dic15C2314yes—
117#6712C2314yes—
118#6712C2314yes—
119C5×Dic3⋊C4C2314yes—
120C5×Dic3⋊C4C2314yes—
121C5×Dic3⋊C4C2314yes—
122C5×Dic3⋊C4C2314yes—
123C4×C5×Dic3C2314yes—
124C3×#683C2314yes—
125C3×#683C2314yes—
126C3×#683C2314yes—
127C3×#683C2314yes—
128C3×C4×Dic5C2314yes—
129Dic3⋊Dic5C2314yes—
130Dic3⋊Dic5C2314yes—
131Dic3⋊Dic5C2314yes—
132#6669C2314yes—
133#6669C2314yes—
134#6669C2314yes—
135#6668C2314yes—
136#6668C2314yes—
137#6668C2314yes—
138#6667C2314yes—
139#6667C2314yes—
140Dic3×Dic5C2314yes—
141Dic3×Dic5C2314yes—
142C2×C3×C4⋊Q8—51no—
143C2×#946—51no—
144C2×#946—51no—
145C2×#944—51no—
146C2×#944D511yescharacteristic, complemented
147#5729—516no—
148C2×#896—51no—
149C2×#896—51no—
150C2×#892—51no—
151C2×D3×C4⋊C4—51no—
152C2×#890—51no—
153C2×#889—51no—
154C2×#889—51no—
155C2×#888—51no—
156C2×#872—51no—
157C2×#870—51no—
158C22×C5×Q8—31no—
159C22×C5×Q8C2×D311yescharacteristic
160C22×C4×D5—31no—
161C22×C4×D5—31no—
162C22×C4×D5—31no—
163C22×Dic10—31no—
164C22×Dic10C2×D311yescharacteristic
165C5×C4⋊Q8—38no—
166C2×C5×C4⋊C4—31no—
167C2×C5×C4⋊C4—31no—
168C2×C5×C4⋊C4—31no—
169C2×C5×C4⋊C4—31no—
170C2×C42×C5—31no—
171#4092—38no—
172#4092—38no—
173#4090—38no—
174#4090C2×D318yescomplemented
175C2×#685—31no—
176C2×#685—31no—
177C2×#685—31no—
178C2×#685—31no—
179C2×C4⋊Dic5—31no—
180C2×C4⋊Dic5—31no—
181C2×C4⋊Dic5—31no—
182C2×C4⋊Dic5—31no—
183C2×#683—31no—
184C2×#683—31no—
185C2×#683—31no—
186C2×#683—31no—
187C2×#683—31no—
188C2×#683—31no—
189C2×#683—31no—
190C2×#683—31no—
191C2×#683C2×D311yescharacteristic
192C2×#683C2×D311yescharacteristic
193C2×#683C2×D311yescharacteristic
194C2×#683C2×D311yescharacteristic
195C2×C4×Dic5—31no—
196C2×C4×Dic5—31no—
197C2×C4×Dic5C2×D311yescharacteristic
198#4042—38no—
199#4042—38no—
200#4038—38no—
201D5×C4⋊C4—38no—
202#4036—38no—
203#4035—38no—
204#4035—38no—
205#4034—38no—
206#4018—38no—
207#4016—38no—
208C2×#544—151noSylow
209C23×C3×C5C2411yescharacteristic
210C22×D15—22no—
211C22×D15—22no—
212C22×D15C2×Q814yes—
213C22×D15C2412yes—
214C3×C5×Q8—44no—
215C2×C3×C4×C5—22no—
216C2×C3×C4×C5—22no—
217C2×C3×C4×C5—22no—
218C2×C3×C4×C5C2412yes—
219C2×C3×C4×C5C2412yes—
220C2×C3×C4×C5C2412yes—
221C2×Dic15—22no—
222C2×Dic15—22no—
223C2×Dic15—22no—
224C2×Dic15C2412yes—
225C2×Dic15C2412yes—
226C2×Dic15C2412yes—
227C4×D15—44no—
228C2×C5×Dic3—22no—
229C2×C5×Dic3—22no—
230C2×C5×Dic3—22no—
231C2×C5×Dic3C2×Q814yes—
232C2×C5×Dic3C2412yes—
233C2×C5×Dic3C2412yes—
234C2×C5×Dic3C2412yes—
235C2×C5×Dic3C2412yes—
236C5×Dic6—44no—
237C2×C3×Dic5—22no—
238C2×C3×Dic5—22no—
239C2×C3×Dic5—22no—
240C2×C3×Dic5C2×Q814yes—
241C2×C3×Dic5C2412yes—
242C2×C3×Dic5C2412yes—
243C2×C3×Dic5C2412yes—
244C2×C3×Dic5C2412yes—
245C3×Dic10—44no—
246#1204—44no—
247#1200—44no—
248#1200C2×Q8116yescomplemented
249C22×C3×Q8—51no—
250C22×C3×Q8C2×D511yescharacteristic
251C22×C4×D3—51no—
252C22×C4×D3—51no—
253C22×C4×D3—51no—
254C22×Dic6—51no—
255C22×Dic6C2×D511yescharacteristic
256C3×C4⋊Q8—58no—
257C2×C3×C4⋊C4—51no—
258C2×C3×C4⋊C4—51no—
259C2×C3×C4⋊C4—51no—
260C2×C3×C4⋊C4—51no—
261C2×C3×C42—51no—
262#946—58no—
263#946—58no—
264#944—58no—
265#944C2×D518yescomplemented
266C2×(C2×D3)⋊C4—51no—
267C2×(C2×D3)⋊C4—51no—
268C2×(C2×D3)⋊C4—51no—
269C2×(C2×D3)⋊C4—51no—
270C2×C4⋊Dic3—51no—
271C2×C4⋊Dic3—51no—
272C2×C4⋊Dic3—51no—
273C2×C4⋊Dic3—51no—
274C2×Dic3⋊C4—51no—
275C2×Dic3⋊C4—51no—
276C2×Dic3⋊C4—51no—
277C2×Dic3⋊C4—51no—
278C2×Dic3⋊C4—51no—
279C2×Dic3⋊C4—51no—
280C2×Dic3⋊C4—51no—
281C2×Dic3⋊C4—51no—
282C2×Dic3⋊C4C2×D511yescharacteristic
283C2×Dic3⋊C4C2×D511yescharacteristic
284C2×Dic3⋊C4C2×D511yescharacteristic
285C2×Dic3⋊C4C2×D511yescharacteristic
286C2×C4×Dic3—51no—
287C2×C4×Dic3—51no—
288C2×C4×Dic3C2×D511yescharacteristic
289#896—58no—
290#896—58no—
291#892—58no—
292D3×C4⋊C4—58no—
293#890—58no—
294#889—58no—
295#889—58no—
296#888—58no—
297#872—58no—
298#870—58no—
299C23×D5—31no—
300C2×C5×Q8—34no—
301C2×C5×Q8—42no—
302C2×C5×Q8—122no—
303C2×C5×Q8C22×D314yes—
304C22×C4×C5—31no—
305C22×C4×C5—31no—
306C22×C4×C5—31no—
307C22×C4×C5—31no—
308C22×C4×C5C22×D311yescharacteristic
309C22×C4×C5C22×D311yescharacteristic
310C22×C4×C5C22×D311yescharacteristic
311C22×Dic5—31no—
312C22×Dic5—31no—
313C22×Dic5—31no—
314C22×Dic5C22×D311yescharacteristic
315C22×Dic5C22×D311yescharacteristic
316C22×Dic5C22×D311yescharacteristic
317C22×Dic5C22×D311yescharacteristic
318C2×C4×D5—38no—
319C2×C4×D5—34no—
320C2×C4×D5—34no—
321C2×C4×D5—34no—
322C2×C4×D5—122no—
323C2×C4×D5—122no—
324C2×Dic10—34no—
325C2×Dic10—42no—
326C2×Dic10—122no—
327C2×Dic10C22×D314yes—
328C5×C4⋊C4—34no—
329C5×C4⋊C4—34no—
330C5×C4⋊C4—34no—
331C5×C4⋊C4—34no—
332C42×C5—34no—
333#685—34no—
334#685—34no—
335#685—34no—
336#685—34no—
337C4⋊Dic5—34no—
338C4⋊Dic5—34no—
339C4⋊Dic5—34no—
340C4⋊Dic5—34no—
341#683—34no—
342#683—34no—
343#683—34no—
344#683—34no—
345#683—34no—
346#683—34no—
347#683—34no—
348#683—34no—
349#683C22×D314yes—
350#683C22×D314yes—
351#683C22×D314yes—
352#683C22×D314yes—
353C4×Dic5—34no—
354C4×Dic5—34no—
355C4×Dic5C22×D314yes—
356#544—1516no—
357C2×C4⋊Q8—31no—
358C2×C4⋊Q8—51no—
359C2×C4⋊Q8—151no—
360C2×C4⋊Q8—151no—
361C2×#125—151no—
362C2×#125—151no—
363C2×#125—151no—
364C2×#125—151no—
365C2×C22⋊Q8—151no—
366C2×C22⋊Q8—151no—
367C2×C22⋊Q8—151no—
368C2×C22⋊Q8—151no—
369C2×#117—151no—
370C2×#117—151no—
371C22×C4⋊C4—151no—
372C22×C3×C5C22×Q812yes—
373C22×C3×C5H(5,𝔽2)12yes—
374C22×C3×C52−1+412yes—
375C22×C3×C5C2511yescharacteristic
376C2×D15—28no—
377C2×D15—22no—
378C2×D15—22no—
379C2×D15C22×Q814yes—
380C3×C4×C5—22no—
381C3×C4×C5—22no—
382C3×C4×C5—22no—
383Dic15—22no—
384Dic15—22no—
385Dic15—22no—
386C3×Dic5—22no—
387C3×Dic5—22no—
388C3×Dic5—22no—
389C3×Dic5C22×Q814yes—
390C5×Dic3—22no—
391C5×Dic3—22no—
392C5×Dic3—22no—
393C5×Dic3C22×Q814yes—
394C23×D3—51no—
395C2×C3×Q8—42no—
396C2×C3×Q8—54no—
397C2×C3×Q8—202no—
398C2×C3×Q8C22×D514yes—
399C22×C3×C4—51no—
400C22×C3×C4—51no—
401C22×C3×C4—51no—
402C22×C3×C4—51no—
403C22×C3×C4C22×D511yescharacteristic
404C22×C3×C4C22×D511yescharacteristic
405C22×C3×C4C22×D511yescharacteristic
406C22×Dic3—51no—
407C22×Dic3—51no—
408C22×Dic3—51no—
409C22×Dic3C22×D511yescharacteristic
410C22×Dic3C22×D511yescharacteristic
411C22×Dic3C22×D511yescharacteristic
412C22×Dic3C22×D511yescharacteristic
413C2×C4×D3—58no—
414C2×C4×D3—54no—
415C2×C4×D3—54no—
416C2×C4×D3—54no—
417C2×C4×D3—202no—
418C2×C4×D3—202no—
419C2×Dic6—42no—
420C2×Dic6—54no—
421C2×Dic6—202no—
422C2×Dic6C22×D514yes—
423C3×C4⋊C4—54no—
424C3×C4⋊C4—54no—
425C3×C4⋊C4—54no—
426C3×C4⋊C4—54no—
427C3×C42—54no—
428(C2×D3)⋊C4—54no—
429(C2×D3)⋊C4—54no—
430(C2×D3)⋊C4—54no—
431(C2×D3)⋊C4—54no—
432C4⋊Dic3—54no—
433C4⋊Dic3—54no—
434C4⋊Dic3—54no—
435C4⋊Dic3—54no—
436Dic3⋊C4—54no—
437Dic3⋊C4—54no—
438Dic3⋊C4—54no—
439Dic3⋊C4—54no—
440Dic3⋊C4—54no—
441Dic3⋊C4—54no—
442Dic3⋊C4—54no—
443Dic3⋊C4—54no—
444Dic3⋊C4C22×D514yes—
445Dic3⋊C4C22×D514yes—
446Dic3⋊C4C22×D514yes—
447Dic3⋊C4C22×D514yes—
448C4×Dic3—54no—
449C4×Dic3—54no—
450C4×Dic3C22×D514yes—
451C23×C5C23×D311yescharacteristic
452C22×D5—34no—
453C22×D5—32no—
454C22×D5—62no—
455C22×D5—62no—
456C5×Q8—44no—
457C5×Q8—124no—
458C2×C4×C5—22no—
459C2×C4×C5—22no—
460C2×C4×C5—22no—
461C2×C4×C5—34no—
462C2×C4×C5—32no—
463C2×C4×C5—32no—
464C2×C4×C5—32no—
465C2×C4×C5—32no—
466C2×C4×C5—62no—
467C2×C4×C5—62no—
468C2×C4×C5—62no—
469C2×C4×C5C23×D312yes—
470C2×C4×C5C23×D312yes—
471C2×C4×C5C23×D312yes—
472C2×Dic5—22no—
473C2×Dic5—22no—
474C2×Dic5—22no—
475C2×Dic5—32no—
476C2×Dic5—32no—
477C2×Dic5—32no—
478C2×Dic5—62no—
479C2×Dic5—62no—
480C2×Dic5—62no—
481C2×Dic5D3×Q814yes—
482C2×Dic5C23×D312yes—
483C2×Dic5C23×D312yes—
484C2×Dic5C23×D312yes—
485C2×Dic5C23×D312yes—
486C4×D5—316no—
487C4×D5—124no—
488C4×D5—124no—
489Dic10—44no—
490Dic10—124no—
491C22×Q8—31no—
492C22×Q8—51no—
493C22×Q8—151no—
494C22×Q8D3×D511yescharacteristic
495C23×C4—151no—
496C23×C4—151no—
497C23×C4—151no—
498C4⋊Q8—38no—
499C4⋊Q8—58no—
500C4⋊Q8—158no—
501C4⋊Q8—158no—
502#125—158no—
503#125—158no—
504#125—158no—
505#125—158no—
506C22⋊Q8—158no—
507C22⋊Q8—158no—
508C22⋊Q8—158no—
509C22⋊Q8—158no—
510#117—158no—
511#117—158no—
512C2×C4⋊C4—31no—
513C2×C4⋊C4—31no—
514C2×C4⋊C4—31no—
515C2×C4⋊C4—31no—
516C2×C4⋊C4—51no—
517C2×C4⋊C4—51no—
518C2×C4⋊C4—51no—
519C2×C4⋊C4—51no—
520C2×C4⋊C4—158no—
521C2×C4⋊C4—151no—
522C2×C4⋊C4—151no—
523C2×C4⋊C4—151no—
524C2×C4⋊C4—151no—
525C2×C4⋊C4—151no—
526C2×C4⋊C4—151no—
527C2×C4⋊C4—151no—
528C2×C4⋊C4—151no—
529C2×C4⋊C4—151no—
530C2×C4⋊C4—151no—
531C2×C4⋊C4—151no—
532C2×C4⋊C4—151no—
533C2×C22⋊C4—151no—
534C2×C22⋊C4—151no—
535C2×C22⋊C4—151no—
536C2×C22⋊C4—151no—
537C2×C42—31no—
538C2×C42—51no—
539C2×C42—151no—
540C2×C42—151no—
541C2×C3×C5#54414yescomplemented
542C2×C3×C5C23×Q811yescharacteristic
543C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
544C2×C3×C5C2×2−1+411yescharacteristic
545D15—24no—
546C23×C3C23×D511yescharacteristic
547C22×D3—54no—
548C22×D3—52no—
549C22×D3—102no—
550C22×D3—102no—
551C3×Q8—44no—
552C3×Q8—204no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—54no—
557C2×C3×C4—52no—
558C2×C3×C4—52no—
559C2×C3×C4—52no—
560C2×C3×C4—52no—
561C2×C3×C4—102no—
562C2×C3×C4—102no—
563C2×C3×C4—102no—
564C2×C3×C4C23×D512yes—
565C2×C3×C4C23×D512yes—
566C2×C3×C4C23×D512yes—
567C2×Dic3—22no—
568C2×Dic3—22no—
569C2×Dic3—22no—
570C2×Dic3—52no—
571C2×Dic3—52no—
572C2×Dic3—52no—
573C2×Dic3—102no—
574C2×Dic3—102no—
575C2×Dic3—102no—
576C2×Dic3Q8×D514yes—
577C2×Dic3C23×D512yes—
578C2×Dic3C23×D512yes—
579C2×Dic3C23×D512yes—
580C2×Dic3C23×D512yes—
581C4×D3—516no—
582C4×D3—204no—
583C4×D3—204no—
584Dic6—44no—
585Dic6—204no—
586C22×C5#100412yes—
587C22×C5C2×D3×Q812yes—
588C22×C5#100712yes—
589C22×C5C24×D311yescharacteristic
590C2×D5—34no—
591C2×D5—62no—
592C2×D5—62no—
593C2×D5—68no—
594C4×C5—22no—
595C4×C5—22no—
596C4×C5—22no—
597C4×C5—34no—
598C4×C5—62no—
599C4×C5—62no—
600C4×C5—62no—
601Dic5—22no—
602Dic5—22no—
603Dic5—22no—
604Dic5—62no—
605Dic5—62no—
606Dic5—62no—
607Dic5C2×D3×Q814yes—
608C24—151no—
609C2×Q8—34no—
610C2×Q8—42no—
611C2×Q8—54no—
612C2×Q8—122no—
613C2×Q8—154no—
614C2×Q8—202no—
615C2×Q8—602no—
616C2×Q8C2×D3×D514yes—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—51no—
622C22×C4—51no—
623C22×C4—51no—
624C22×C4—51no—
625C22×C4—154no—
626C22×C4—158no—
627C22×C4—154no—
628C22×C4—151no—
629C22×C4—151no—
630C22×C4—151no—
631C22×C4—154no—
632C22×C4—602no—
633C22×C4—602no—
634C22×C4C2×D3×D511yescharacteristic
635C22×C4C2×D3×D511yescharacteristic
636C22×C4C2×D3×D511yescharacteristic
637C4⋊C4—34no—
638C4⋊C4—34no—
639C4⋊C4—34no—
640C4⋊C4—34no—
641C4⋊C4—54no—
642C4⋊C4—54no—
643C4⋊C4—54no—
644C4⋊C4—54no—
645C4⋊C4—154no—
646C4⋊C4—154no—
647C4⋊C4—154no—
648C4⋊C4—154no—
649C4⋊C4—154no—
650C4⋊C4—154no—
651C4⋊C4—154no—
652C4⋊C4—154no—
653C4⋊C4—154no—
654C4⋊C4—154no—
655C4⋊C4—154no—
656C4⋊C4—154no—
657C22⋊C4—154no—
658C22⋊C4—154no—
659C22⋊C4—154no—
660C22⋊C4—154no—
661C42—34no—
662C42—54no—
663C42—154no—
664C42—154no—
665C3×C5C2×#54411yescharacteristic, complemented, Hall
666C22×C3#414412yes—
667C22×C3C2×Q8×D512yes—
668C22×C3#414712yes—
669C22×C3C24×D511yescharacteristic
670C2×D3—54no—
671C2×D3—108no—
672C2×D3—102no—
673C2×D3—102no—
674C3×C4—22no—
675C3×C4—22no—
676C3×C4—22no—
677C3×C4—54no—
678C3×C4—102no—
679C3×C4—102no—
680C3×C4—102no—
681Dic3—22no—
682Dic3—22no—
683Dic3—22no—
684Dic3—102no—
685Dic3—102no—
686Dic3—102no—
687Dic3C2×Q8×D514yes—
688C2×C5#572914yescomplemented
689C2×C5C2×#100411yescharacteristic
690C2×C5C22×D3×Q811yescharacteristic
691C2×C5C2×#100711yescharacteristic
692D5—64no—
693C23—154no—
694C23—152no—
695C23—302no—
696C23—302no—
697C23C22×D3×D511yescharacteristic
698Q8—44no—
699Q8—124no—
700Q8—204no—
701Q8—604no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—34no—
706C2×C4—32no—
707C2×C4—32no—
708C2×C4—32no—
709C2×C4—32no—
710C2×C4—54no—
711C2×C4—52no—
712C2×C4—52no—
713C2×C4—52no—
714C2×C4—52no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—102no—
719C2×C4—102no—
720C2×C4—102no—
721C2×C4—1516no—
722C2×C4—152no—
723C2×C4—152no—
724C2×C4—152no—
725C2×C4—302no—
726C2×C4—302no—
727C2×C4—302no—
728C2×C4—604no—
729C2×C4—604no—
730C2×C4C22×D3×D512yes—
731C2×C4C22×D3×D512yes—
732C2×C4C22×D3×D512yes—
733C2×C3#6606314yescomplemented
734C2×C3C2×#414411yescharacteristic
735C2×C3C22×Q8×D511yescharacteristic
736C2×C3C2×#414711yescharacteristic
737D3—104no—
738C5C2×#572911yescharacteristic, complemented, Sylow
739C22—154no—
740C22—302no—
741C22—308no—
742C22—302no—
743C22#9202912yes—
744C22D3×Q8×D512yes—
745C22#9204912yes—
746C22C23×D3×D511yescharacteristic
747C4—22no—
748C4—22no—
749C4—22no—
750C4—34no—
751C4—54no—
752C4—62no—
753C4—62no—
754C4—62no—
755C4—102no—
756C4—102no—
757C4—102no—
758C4—302no—
759C4—302no—
760C4—302no—
761C3C2×#6606311yescharacteristic, complemented, Sylow
762C2—304no—
763C2#1175518614yesdirect product factor
764C2C2×#9202911yescharacteristic
765C2C2×D3×Q8×D511yescharacteristic
766C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C24
prime radicalC23×D15C23
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#544
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C5×#944C2semidirect
3. C2×C3×#4090C2semidirect
4. #11755186C2direct (N × H)
10. C2×#91379C2semidirect
11. C2×#91378C2semidirect
13. C2×#91343C2semidirect
14. C2×#91334C2semidirect
15. C2×#91329C2semidirect
16. C2×#91327C2semidirect
31. C5×#944C22semidirect
37. C3×#4090C22semidirect
61. #91379C22semidirect
62. #91378C22semidirect
64. #91343C22semidirect
65. #91334C22semidirect
66. #91329C22semidirect
67. #91327C22semidirect
73. C2×#4090D3semidirect
111. C2×#1200Q8semidirect
146. C2×#944D5semidirect
174. #4090C2×D3semidirect
248. #1200C2×Q8semidirect
265. #944C2×D5semidirect
541. C2×C3×C5#544semidirect
665. C3×C5C2×#544semidirect
688. C2×C5#5729semidirect
733. C2×C3#66063semidirect
738. C5C2×#5729semidirect
761. C3C2×#66063semidirect
763. C2#11755186direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918352
C2×C5×#9442
C2×C3×#40902
#117551862
C2×#914242
C2×#914112
C2×#914042
C2×#914032
C2×#914022
C2×#913792
C2×#913782
C2×#913772
C2×#913432
C2×#913342
C2×#913292
C2×#913272
C2×#660633
C2×#57295