Finite Group Databasebeta

← C2×#11754865 #14481373

Subgroups — C2×#11754865 #14481373

Order 1920.

2264 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91824C211yesmaximal, characteristic, complemented
2C2×C5×#936C211yesmaximal, characteristic, complemented
3C2×C3×#4085C211yesmaximal, characteristic
4C2×#91576C211yesmaximal, characteristic, complemented
5C2×#91574C211yesmaximal, characteristic, complemented
6C2×#91559C211yesmaximal, characteristic, complemented
7C2×#91548C211yesmaximal, characteristic, complemented
8C2×#91534C211yesmaximal, characteristic, complemented
9C2×#91534C211yesmaximal, characteristic, complemented
10C2×#91531C211yesmaximal, characteristic, complemented
11C2×#91528C211yesmaximal, characteristic, complemented
12#11754865C2116yesmaximal, direct product factor
13C2×#91421C211yesmaximal, characteristic, complemented
14C2×#91363C211yesmaximal, characteristic, complemented
15C2×#91329C211yesmaximal, characteristic, complemented
16C2×#91324C211yesmaximal, characteristic, complemented
17C2×#66003—31nomaximal, Hall
18C22×C3×C5×D4C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C22×C5×Dic6C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C22×C3×C22⋊D5C2211yescharacteristic
23C23×C3×Dic5C2211yescharacteristic
24C22×#1204C2211yescharacteristic
25C22×#1204C2211yescharacteristic
26C22×D5×Dic3C2211yescharacteristic
27C2×#6719C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×#6719C2211yescharacteristic
30#91824C2218yescomplemented
31C2×#6712C2211yescharacteristic
32C2×#6712C2211yescharacteristic
33C2×C5×#217C2211yescharacteristic
34C2×C5×#217C2211yescharacteristic
35C2×C5×#217C2211yescharacteristic
36C2×C5×#217C2211yescharacteristic
37C5×#936C2218yescomplemented
38C2×C4×C5×Dic3C2211yescharacteristic
39C2×C3×C22⋊Dic5C2211yescharacteristic
40C3×#4085C2218yes—
41C2×C3×#685C2211yescharacteristic
42C2×C3×#683C2211yescharacteristic
43#91576C2218yescomplemented
44#91574C2218yescomplemented
45#91559C2218yescomplemented
46#91548C2218yescomplemented
47C2×Dic3⋊Dic5C2211yescharacteristic
48C2×Dic3⋊Dic5C2211yescharacteristic
49C2×#6669C2211yescharacteristic
50C2×#6669C2211yescharacteristic
51C2×#6668C2211yescharacteristic
52C2×#6668C2211yescharacteristic
53C2×#6668C2211yescharacteristic
54C2×#6665C2211yescharacteristic
55C2×#6665C2211yescharacteristic
56C2×#6665C2211yescharacteristic
57#91534C2218yescomplemented
58#91534C2218yescomplemented
59#91531C2218yescomplemented
60#91528C2218yescomplemented
61C2×Dic3×Dic5C2211yescharacteristic
62C2×Dic3×Dic5C2211yescharacteristic
63C2×Dic3×Dic5C2211yescharacteristic
64#91421C2218yescomplemented
65#91363C2218yescomplemented
66#91329C2218yescomplemented
67#91324C2218yescomplemented
68C2×#5603—51nomaximal, Hall
69C2×C5×#124—31no—
70C2×#4092—31no—
71C2×#4090—31no—
72C2×#4085D311yescharacteristic
73C2×#4081—31no—
74#66003—316no—
75C2×#4031—31no—
76C2×#4031—31no—
77C2×#4029—31no—
78C2×#4027—31no—
79C2×#4025—31no—
80C2×#4024—31no—
81C2×#4024—31no—
82C2×#4023—31no—
83C2×#4022—31no—
84C2×C4×Dic10—31no—
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C23×C3×D5C2311yescharacteristic
88C2×C3×C5×D4—42no—
89C2×C3×C5×D4C2314yes—
90C22×C3×C4×C5C2311yescharacteristic
91C22×Dic15—42no—
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C22×Dic15C2311yescharacteristic
96C22×Dic15C2314yes—
97C22×C5×Dic3C2311yescharacteristic
98C22×C5×Dic3C2311yescharacteristic
99C22×C5×Dic3C2311yescharacteristic
100C22×C5×Dic3C2311yescharacteristic
101C2×C5×Dic6—42no—
102C2×C5×Dic6C2314yes—
103C2×C3×C22⋊D5—24no—
104C2×C3×C22⋊D5—42no—
105C2×C3×C22⋊D5C2314yes—
106C2×C3×C22⋊D5C2314yes—
107C22×C3×Dic5—24no—
108C22×C3×Dic5C2314yes—
109C22×C3×Dic5C2311yescharacteristic
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C2×#1204—24no—
113C2×#1204—42no—
114C2×#1204C2314yes—
115C2×#1204C2314yes—
116C2×D5×Dic3—42no—
117C2×D5×Dic3C2314yes—
118#6719C2314yes—
119#6719C2314yes—
120#6719C2314yes—
121#6712C2314yes—
122#6712C2314yes—
123C5×#217C2314yes—
124C5×#217C2314yes—
125C5×#217C2314yes—
126C5×#217C2314yes—
127C4×C5×Dic3C2314yes—
128C3×C22⋊Dic5C2314yes—
129C3×#685C2314yes—
130C3×#683C2314yes—
131Dic3⋊Dic5C2314yes—
132Dic3⋊Dic5C2314yes—
133#6669C2314yes—
134#6669C2314yes—
135#6668C2314yes—
136#6668C2314yes—
137#6668C2314yes—
138#6665C2314yes—
139#6665C2314yes—
140#6665C2314yes—
141Dic3×Dic5C2314yes—
142Dic3×Dic5C2314yes—
143Dic3×Dic5C2314yes—
144C2×C3×#121—51no—
145C2×#936—51no—
146C2×#936—51no—
147C2×#936D511yescharacteristic, complemented
148C2×#935—51no—
149C2×#935—51no—
150C2×D4×Dic3—51no—
151C2×#926—51no—
152C2×#924—51no—
153#5603—516no—
154C2×#888—51no—
155C2×#887—51no—
156C2×#879—51no—
157C2×#879—51no—
158C2×#878—51no—
159C2×#878—51no—
160C22×C5×Q8—31no—
161C22×C5×D4C2×D311yescharacteristic
162C22×C22⋊D5C2×D311yescharacteristic
163C22×C22⋊D5C2×D311yescharacteristic
164C23×Dic5—31no—
165C23×Dic5C2×D311yescharacteristic
166C22×C4×D5—31no—
167C22×Dic10—31no—
168C22×Dic10—31no—
169C5×#124—38no—
170C2×C5×C22⋊C4—31no—
171C2×C5×C22⋊C4—31no—
172C2×C5×C22⋊C4—31no—
173C2×C5×C22⋊C4—31no—
174C2×C42×C5—31no—
175C2×C22⋊Dic5—31no—
176C2×C22⋊Dic5—31no—
177C2×C22⋊Dic5—31no—
178C2×C22⋊Dic5C2×D311yescharacteristic
179#4092—38no—
180#4090—38no—
181#4085C2×D318yes—
182#4081—38no—
183C2×#685—31no—
184C2×#685—31no—
185C2×#685—31no—
186C2×#685C2×D311yescharacteristic
187C2×C4⋊Dic5—31no—
188C2×C4⋊Dic5—31no—
189C2×#683—31no—
190C2×#683—31no—
191C2×#683—31no—
192C2×#683—31no—
193C2×#683—31no—
194C2×#683—31no—
195C2×#683—31no—
196C2×#683C2×D311yescharacteristic
197C2×C4×Dic5—31no—
198C2×C4×Dic5—31no—
199C2×C4×Dic5—31no—
200#4031—38no—
201#4031—38no—
202#4029—38no—
203#4027—38no—
204#4025—38no—
205#4024—38no—
206#4024—38no—
207#4023—38no—
208#4022—38no—
209C4×Dic10—38no—
210C2×#542—151noSylow
211C23×C3×C5—22no—
212C23×C3×C5—22no—
213C23×C3×C5—22no—
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5—22no—
217C23×C3×C5C2412yes—
218C23×C3×C5C2412yes—
219C23×C3×C5C2411yescharacteristic
220C22×C3×D5—22no—
221C22×C3×D5—22no—
222C22×C3×D5—22no—
223C22×C3×D5C2412yes—
224C3×C5×D4—44no—
225C2×C3×C4×C5—22no—
226C2×C3×C4×C5C2412yes—
227C2×Dic15—22no—
228C2×Dic15—22no—
229C2×Dic15—22no—
230C2×Dic15—22no—
231C2×Dic15—44no—
232C2×Dic15C2412yes—
233C2×Dic15C2412yes—
234C2×Dic15C2412yes—
235C2×Dic15C2412yes—
236C2×C5×Dic3—22no—
237C2×C5×Dic3—22no—
238C2×C5×Dic3—22no—
239C2×C5×Dic3—22no—
240C2×C5×Dic3C2412yes—
241C2×C5×Dic3C2412yes—
242C2×C5×Dic3C2412yes—
243C2×C5×Dic3C2412yes—
244C5×Dic6—44no—
245C3×C22⋊D5—28no—
246C3×C22⋊D5—44no—
247C2×C3×Dic5—22no—
248C2×C3×Dic5—22no—
249C2×C3×Dic5—28no—
250C2×C3×Dic5#4114yes—
251C2×C3×Dic5C2412yes—
252C2×C3×Dic5C2412yes—
253C2×C3×Dic5C2412yes—
254#1204—28no—
255#1204—44no—
256D5×Dic3—44no—
257C22×C3×D4—51no—
258C22×C3×D4—51no—
259C22×C3×D4C2×D511yescharacteristic
260C23×C3×C4—51no—
261C23×Dic3—51no—
262C23×Dic3—51no—
263C22×Dic6—51no—
264C22×Dic6—51no—
265C22×Dic6C2×D511yescharacteristic
266C3×#121—58no—
267C2×C3×C4⋊C4—51no—
268C2×C3×C22⋊C4—51no—
269C2×C3×C22⋊C4—51no—
270C2×#217—51no—
271C2×#217—51no—
272C2×#217—51no—
273C2×#217—51no—
274C2×#217—51no—
275C2×#217—51no—
276C2×#217C2×D511yescharacteristic
277C2×#217C2×D511yescharacteristic
278C2×#217C2×D511yescharacteristic
279C2×#217C2×D511yescharacteristic
280#936—58no—
281#936—58no—
282#936C2×D518yescomplemented
283#935—58no—
284#935—58no—
285D4×Dic3—58no—
286#926—58no—
287C2×C4⋊Dic3—51no—
288C2×C4⋊Dic3—51no—
289C2×C4⋊Dic3—51no—
290#924—58no—
291C2×Dic3⋊C4—51no—
292C2×Dic3⋊C4—51no—
293C2×Dic3⋊C4—51no—
294C2×Dic3⋊C4—51no—
295C2×Dic3⋊C4—51no—
296C2×Dic3⋊C4—51no—
297C2×C4×Dic3—51no—
298C2×C4×Dic3—51no—
299C2×C4×Dic3—51no—
300C2×C4×Dic3C2×D511yescharacteristic
301#888—58no—
302#887—58no—
303#879—58no—
304#879—58no—
305#878—58no—
306#878—58no—
307C24×C5C22×D311yescharacteristic
308C24×C5C22×D311yescharacteristic
309C23×D5C22×D311yescharacteristic
310C2×C5×Q8—34no—
311C2×C5×Q8—122no—
312C2×C5×D4—42no—
313C2×C5×D4C22×D314yes—
314C22×C4×C5—31no—
315C22×C4×C5—31no—
316C22×C4×C5—31no—
317C22×C4×C5—31no—
318C22×C4×C5C22×D311yescharacteristic
319C2×C22⋊D5—24no—
320C2×C22⋊D5—42no—
321C2×C22⋊D5C22×D314yes—
322C2×C22⋊D5C22×D314yes—
323C22×Dic5—24no—
324C22×Dic5—31no—
325C22×Dic5—31no—
326C22×Dic5—31no—
327C22×Dic5—31no—
328C22×Dic5—34no—
329C22×Dic5—122no—
330C22×Dic5C22×D311yescharacteristic
331C22×Dic5C22×D311yescharacteristic
332C22×Dic5C22×D314yes—
333C22×Dic5C22×D311yescharacteristic
334C2×C4×D5—34no—
335C2×C4×D5—122no—
336C2×Dic10—34no—
337C2×Dic10—34no—
338C2×Dic10—64no—
339C2×Dic10—122no—
340C5×C22⋊C4—34no—
341C5×C22⋊C4—34no—
342C5×C22⋊C4—34no—
343C5×C22⋊C4—34no—
344C42×C5—34no—
345C22⋊Dic5—34no—
346C22⋊Dic5—34no—
347C22⋊Dic5—34no—
348C22⋊Dic5C22×D314yes—
349#685—34no—
350#685—34no—
351#685—34no—
352#685C22×D314yes—
353C4⋊Dic5—34no—
354C4⋊Dic5—34no—
355#683—34no—
356#683—34no—
357#683—34no—
358#683—34no—
359#683—34no—
360#683—34no—
361#683—34no—
362#683C22×D314yes—
363C4×Dic5—34no—
364C4×Dic5—34no—
365C4×Dic5—34no—
366#542—1516no—
367C2×C4⋊Q8—151no—
368C2×#126—151no—
369C2×#126—151no—
370C2×#124—31no—
371C2×#124—151no—
372C2×#124—151no—
373C2×#123—151no—
374C2×#123—151no—
375C2×C22⋊Q8—151no—
376C2×C22⋊Q8—151no—
377C2×C22⋊Q8—151no—
378C2×#121—51no—
379C2×C4×Q8—151no—
380C2×C4×D4—151no—
381C2×#117—151no—
382C22×C3×C5—22no—
383C22×C3×C5—22no—
384C22×C3×C5—22no—
385C22×C3×C5—22no—
386C22×C3×C5—22no—
387C22×C3×C5—22no—
388C22×C3×C5—44no—
389C22×C3×C5—44no—
390C22×C3×C5C2×#4112yes—
391C22×C3×C5H(5,𝔽2)12yes—
392C22×C3×C52−1+412yes—
393C22×C3×C5C2511yescharacteristic
394C2×C3×D5—22no—
395C2×C3×D5—22no—
396C2×C3×D5—22no—
397C2×C3×D5—44no—
398C3×C4×C5—22no—
399Dic15—22no—
400Dic15—22no—
401Dic15—22no—
402Dic15—22no—
403C3×Dic5—22no—
404C3×Dic5—22no—
405C3×Dic5C2×#4114yes—
406C5×Dic3—22no—
407C5×Dic3—22no—
408C5×Dic3—22no—
409C5×Dic3—22no—
410C24×C3—51no—
411C24×C3C22×D511yescharacteristic
412C24×C3C22×D511yescharacteristic
413C2×C3×D4—42no—
414C2×C3×D4—54no—
415C2×C3×D4—54no—
416C2×C3×D4—104no—
417C2×C3×D4—202no—
418C2×C3×D4C22×D514yes—
419C22×C3×C4—51no—
420C22×C3×C4—51no—
421C22×C3×C4—51no—
422C22×C3×C4—54no—
423C22×C3×C4—104no—
424C22×C3×C4C22×D511yescharacteristic
425C22×Dic3—51no—
426C22×Dic3—51no—
427C22×Dic3—51no—
428C22×Dic3—51no—
429C22×Dic3—54no—
430C22×Dic3—54no—
431C22×Dic3—202no—
432C22×Dic3—202no—
433C22×Dic3C22×D511yescharacteristic
434C22×Dic3C22×D511yescharacteristic
435C22×Dic3C22×D511yescharacteristic
436C22×Dic3C22×D511yescharacteristic
437C2×Dic6—42no—
438C2×Dic6—54no—
439C2×Dic6—54no—
440C2×Dic6—104no—
441C2×Dic6—202no—
442C2×Dic6C22×D514yes—
443C3×C4⋊C4—54no—
444C3×C22⋊C4—54no—
445C3×C22⋊C4—54no—
446#217—54no—
447#217—54no—
448#217—54no—
449#217—54no—
450#217—54no—
451#217—54no—
452#217C22×D514yes—
453#217C22×D514yes—
454#217C22×D514yes—
455#217C22×D514yes—
456C4⋊Dic3—54no—
457C4⋊Dic3—54no—
458C4⋊Dic3—54no—
459Dic3⋊C4—54no—
460Dic3⋊C4—54no—
461Dic3⋊C4—54no—
462Dic3⋊C4—54no—
463Dic3⋊C4—54no—
464Dic3⋊C4—54no—
465C4×Dic3—54no—
466C4×Dic3—54no—
467C4×Dic3—54no—
468C4×Dic3C22×D514yes—
469C23×C5—22no—
470C23×C5—22no—
471C23×C5—22no—
472C23×C5—22no—
473C23×C5—22no—
474C23×C5—22no—
475C23×C5C23×D312yes—
476C23×C5C23×D312yes—
477C23×C5C23×D311yescharacteristic
478C22×D5—22no—
479C22×D5—22no—
480C22×D5—22no—
481C22×D5C23×D312yes—
482C5×Q8—124no—
483C5×D4—44no—
484C2×C4×C5—22no—
485C2×C4×C5—32no—
486C2×C4×C5—32no—
487C2×C4×C5—32no—
488C2×C4×C5—32no—
489C2×C4×C5—62no—
490C2×C4×C5—62no—
491C2×C4×C5—62no—
492C2×C4×C5—62no—
493C2×C4×C5C23×D312yes—
494C22⋊D5—28no—
495C22⋊D5—44no—
496C2×Dic5—22no—
497C2×Dic5—22no—
498C2×Dic5—28no—
499C2×Dic5—32no—
500C2×Dic5—32no—
501C2×Dic5—32no—
502C2×Dic5—32no—
503C2×Dic5—62no—
504C2×Dic5—62no—
505C2×Dic5—62no—
506C2×Dic5—62no—
507C2×Dic5—124no—
508C2×Dic5#23714yes—
509C2×Dic5C23×D312yes—
510C2×Dic5C23×D312yes—
511C2×Dic5C23×D312yes—
512C4×D5—124no—
513Dic10—68no—
514Dic10—124no—
515C22×Q8—31no—
516C22×Q8—151no—
517C22×Q8—151no—
518C22×D4—51no—
519C22×D4—51no—
520C22×D4D3×D511yescharacteristic
521C23×C4—51no—
522C23×C4—151no—
523C23×C4—151no—
524C4⋊Q8—158no—
525#126—158no—
526#126—158no—
527#124—38no—
528#124—158no—
529#124—158no—
530#123—158no—
531#123—158no—
532C22⋊Q8—158no—
533C22⋊Q8—158no—
534C22⋊Q8—158no—
535#121—58no—
536C4×Q8—158no—
537C4×D4—158no—
538#117—158no—
539C2×C4⋊C4—51no—
540C2×C4⋊C4—151no—
541C2×C4⋊C4—151no—
542C2×C4⋊C4—151no—
543C2×C4⋊C4—151no—
544C2×C4⋊C4—151no—
545C2×C4⋊C4—151no—
546C2×C4⋊C4—151no—
547C2×C4⋊C4—151no—
548C2×C4⋊C4—151no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—31no—
553C2×C22⋊C4—51no—
554C2×C22⋊C4—51no—
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×C42—31no—
562C2×C42—151no—
563C2×C42—151no—
564C2×C42—151no—
565C2×C3×C5—42no—
566C2×C3×C5—42no—
567C2×C3×C5#54214yescomplemented
568C2×C3×C5C22×#4111yescharacteristic
569C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
570C2×C3×C5C2×2−1+411yescharacteristic
571C3×D5—42no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—22no—
576C23×C3—22no—
577C23×C3—22no—
578C23×C3—52no—
579C23×C3—102no—
580C23×C3—102no—
581C23×C3—102no—
582C23×C3C23×D512yes—
583C23×C3C23×D512yes—
584C23×C3C23×D511yescharacteristic
585C3×D4—44no—
586C3×D4—108no—
587C3×D4—204no—
588C2×C3×C4—22no—
589C2×C3×C4—54no—
590C2×C3×C4—52no—
591C2×C3×C4—52no—
592C2×C3×C4—52no—
593C2×C3×C4—108no—
594C2×C3×C4—102no—
595C2×C3×C4—102no—
596C2×C3×C4C23×D512yes—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—52no—
602C2×Dic3—52no—
603C2×Dic3—52no—
604C2×Dic3—52no—
605C2×Dic3—102no—
606C2×Dic3—102no—
607C2×Dic3—102no—
608C2×Dic3—102no—
609C2×Dic3—204no—
610C2×Dic3—204no—
611C2×Dic3C23×D512yes—
612C2×Dic3C23×D512yes—
613C2×Dic3C23×D512yes—
614C2×Dic3C23×D512yes—
615Dic6—44no—
616Dic6—108no—
617Dic6—204no—
618C22×C5—22no—
619C22×C5—22no—
620C22×C5—22no—
621C22×C5—22no—
622C22×C5—22no—
623C22×C5—22no—
624C22×C5—44no—
625C22×C5—44no—
626C22×C5C2×#23712yes—
627C22×C5#100412yes—
628C22×C5#101012yes—
629C22×C5C24×D311yescharacteristic
630C2×D5—22no—
631C2×D5—22no—
632C2×D5—22no—
633C2×D5—44no—
634C4×C5—22no—
635C4×C5—62no—
636C4×C5—62no—
637C4×C5—62no—
638C4×C5—62no—
639Dic5—22no—
640Dic5—22no—
641Dic5—62no—
642Dic5—62no—
643Dic5—62no—
644Dic5—62no—
645Dic5C2×#23714yes—
646C24—51no—
647C24C2×D3×D511yescharacteristic
648C24C2×D3×D511yescharacteristic
649C2×Q8—34no—
650C2×Q8—122no—
651C2×Q8—154no—
652C2×Q8—154no—
653C2×Q8—304no—
654C2×Q8—602no—
655C2×D4—42no—
656C2×D4—54no—
657C2×D4—54no—
658C2×D4—104no—
659C2×D4—202no—
660C2×D4C2×D3×D514yes—
661C22×C4—31no—
662C22×C4—31no—
663C22×C4—31no—
664C22×C4—31no—
665C22×C4—51no—
666C22×C4—54no—
667C22×C4—51no—
668C22×C4—51no—
669C22×C4—104no—
670C22×C4—154no—
671C22×C4—151no—
672C22×C4—151no—
673C22×C4—151no—
674C22×C4—151no—
675C22×C4—154no—
676C22×C4—602no—
677C22×C4—602no—
678C22×C4C2×D3×D511yescharacteristic
679C4⋊C4—54no—
680C4⋊C4—154no—
681C4⋊C4—154no—
682C4⋊C4—154no—
683C4⋊C4—154no—
684C4⋊C4—154no—
685C4⋊C4—154no—
686C4⋊C4—154no—
687C4⋊C4—154no—
688C4⋊C4—154no—
689C22⋊C4—34no—
690C22⋊C4—34no—
691C22⋊C4—34no—
692C22⋊C4—34no—
693C22⋊C4—54no—
694C22⋊C4—54no—
695C22⋊C4—154no—
696C22⋊C4—154no—
697C22⋊C4—154no—
698C22⋊C4—154no—
699C22⋊C4—154no—
700C22⋊C4—154no—
701C42—34no—
702C42—154no—
703C42—154no—
704C42—154no—
705C3×C5C2×#54211yescharacteristic, complemented, Hall
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—44no—
713C22×C3—44no—
714C22×C3—102no—
715C22×C3—102no—
716C22×C3—102no—
717C22×C3—204no—
718C22×C3#414412yes—
719C22×C3D5×#4112yes—
720C22×C3#415012yes—
721C22×C3C24×D511yescharacteristic
722C3×C4—22no—
723C3×C4—54no—
724C3×C4—102no—
725C3×C4—102no—
726Dic3—22no—
727Dic3—22no—
728Dic3—22no—
729Dic3—22no—
730Dic3—102no—
731Dic3—102no—
732Dic3—102no—
733Dic3—102no—
734C2×C5—42no—
735C2×C5—42no—
736C2×C5#560314yescomplemented
737C2×C5C22×#23711yescharacteristic
738C2×C5C2×#100411yescharacteristic
739C2×C5C2×#101011yescharacteristic
740D5—42no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—52no—
748C23—102no—
749C23—102no—
750C23—102no—
751C23C22×D3×D512yes—
752C23C22×D3×D512yes—
753C23C22×D3×D511yescharacteristic
754Q8—124no—
755Q8—308no—
756Q8—604no—
757D4—44no—
758D4—108no—
759D4—204no—
760C2×C4—22no—
761C2×C4—32no—
762C2×C4—32no—
763C2×C4—32no—
764C2×C4—32no—
765C2×C4—54no—
766C2×C4—52no—
767C2×C4—52no—
768C2×C4—52no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—108no—
774C2×C4—102no—
775C2×C4—102no—
776C2×C4—152no—
777C2×C4—152no—
778C2×C4—152no—
779C2×C4—152no—
780C2×C4—302no—
781C2×C4—302no—
782C2×C4—302no—
783C2×C4—302no—
784C2×C4—604no—
785C2×C4—604no—
786C2×C4C22×D3×D512yes—
787C2×C3—42no—
788C2×C3—42no—
789C2×C3—202no—
790C2×C3#6600314yescomplemented
791C2×C3C2×#414411yescharacteristic
792C2×C3C2×D5×#4111yescharacteristic
793C2×C3C2×#415011yescharacteristic
794C5C2×#560311yescharacteristic, complemented, Sylow
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—44no—
802C22—44no—
803C22—102no—
804C22—102no—
805C22—102no—
806C22—204no—
807C22#9202012yes—
808C22D5×#23712yes—
809C22#9204912yes—
810C22C23×D3×D511yescharacteristic
811C4—22no—
812C4—54no—
813C4—62no—
814C4—62no—
815C4—62no—
816C4—62no—
817C4—102no—
818C4—102no—
819C4—302no—
820C4—302no—
821C4—302no—
822C4—302no—
823C3C2×#6600311yescharacteristic, complemented, Sylow
824C2—42no—
825C2—42no—
826C2—202no—
827C2#1175486514yesdirect product factor
828C2C2×#9202011yescharacteristic
829C2C2×D5×#23711yescharacteristic
830C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
prime radicalC2×C3×#4085C2
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#542
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#91824C2semidirect
2. C2×C5×#936C2semidirect
4. C2×#91576C2semidirect
5. C2×#91574C2semidirect
6. C2×#91559C2semidirect
7. C2×#91548C2semidirect
8. C2×#91534C2semidirect
9. C2×#91534C2semidirect
10. C2×#91531C2semidirect
11. C2×#91528C2semidirect
12. #11754865C2direct (N × H)
13. C2×#91421C2semidirect
14. C2×#91363C2semidirect
15. C2×#91329C2semidirect
16. C2×#91324C2semidirect
30. #91824C22semidirect
37. C5×#936C22semidirect
43. #91576C22semidirect
44. #91574C22semidirect
45. #91559C22semidirect
46. #91548C22semidirect
57. #91534C22semidirect
58. #91534C22semidirect
59. #91531C22semidirect
60. #91528C22semidirect
64. #91421C22semidirect
65. #91363C22semidirect
66. #91329C22semidirect
67. #91324C22semidirect
147. C2×#936D5semidirect
282. #936C2×D5semidirect
567. C2×C3×C5#542semidirect
705. C3×C5C2×#542semidirect
736. C2×C5#5603semidirect
790. C2×C3#66003semidirect
794. C5C2×#5603semidirect
823. C3C2×#66003semidirect
827. C2#11754865direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918242
C2×C5×#9362
C2×C3×#40852
C2×#915762
C2×#915742
C2×#915592
C2×#915482
C2×#915342
C2×#915312
C2×#915282
#117548652
C2×#914212
C2×#913632
C2×#913292
C2×#913242
C2×#660033
C2×#56035