Finite Group Databasebeta

← C2×#11754890 #14481376

Subgroups — C2×#11754890 #14481376

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×#91825C211yesmaximal, characteristic, complemented
2C2×C5×#939C211yesmaximal, characteristic
3C2×C3×#4081C211yesmaximal, characteristic, complemented
4C2×#91575C211yesmaximal, characteristic, complemented
5C2×#91574C211yesmaximal, characteristic, complemented
6C2×#91555C211yesmaximal, characteristic, complemented
7C2×Dic5×#67C211yesmaximal, characteristic, complemented
8C2×#91531C211yesmaximal, characteristic, complemented
9C2×#91529C211yesmaximal, characteristic, complemented
10C2×#91525C211yesmaximal, characteristic, complemented
11C2×#91525C211yesmaximal, characteristic, complemented
12#11754890C2116yesmaximal, direct product factor
13C2×#91432C211yesmaximal, characteristic, complemented
14C2×#91367C211yesmaximal, characteristic, complemented
15C2×#91328C211yesmaximal, characteristic, complemented
16C2×#91325C211yesmaximal, characteristic, complemented
17C2×#65937—31nomaximal, Hall
18C22×C3×C5×D4C2211yescharacteristic
19C22×Dic30C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C22×C5×#67C2211yescharacteristic
22C23×C5×Dic3C2211yescharacteristic
23C23×C3×Dic5C2211yescharacteristic
24C22×#1204C2211yescharacteristic
25C22×#1204C2211yescharacteristic
26C22×D3×Dic5C2211yescharacteristic
27C2×#6719C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×#6719C2211yescharacteristic
30C2×#6719C2211yescharacteristic
31#91825C2218yescomplemented
32C2×C4×Dic15C2211yescharacteristic
33C2×C5×#217C2211yescharacteristic
34C5×#939C2218yes—
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic
36C2×C5×Dic3⋊C4C2211yescharacteristic
37C2×C3×C22⋊Dic5C2211yescharacteristic
38C2×C3×C22⋊Dic5C2211yescharacteristic
39C2×C3×C22⋊Dic5C2211yescharacteristic
40C3×#4081C2218yescomplemented
41C2×C3×#683C2211yescharacteristic
42C2×C3×#683C2211yescharacteristic
43#91575C2218yescomplemented
44#91574C2218yescomplemented
45#91555C2218yescomplemented
46Dic5×#67C2218yescomplemented
47C2×Dic3⋊Dic5C2211yescharacteristic
48C2×Dic3⋊Dic5C2211yescharacteristic
49C2×Dic3⋊Dic5C2211yescharacteristic
50C2×#6669C2211yescharacteristic
51C2×#6669C2211yescharacteristic
52C2×#6668C2211yescharacteristic
53C2×#6668C2211yescharacteristic
54C2×(C2×D3)⋊Dic5C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2211yescharacteristic
56C2×(C2×D3)⋊Dic5C2211yescharacteristic
57#91531C2218yescomplemented
58#91529C2218yescomplemented
59C2×Dic3×Dic5C2211yescharacteristic
60C2×Dic3×Dic5C2211yescharacteristic
61C2×Dic3×Dic5C2211yescharacteristic
62#91525C2218yescomplemented
63#91525C2218yescomplemented
64#91432C2218yescomplemented
65#91367C2218yescomplemented
66#91328C2218yescomplemented
67#91325C2218yescomplemented
68C2×#5662—51nomaximal, Hall
69C2×C5×#121—31no—
70C2×#4082—31no—
71C2×#4082—31no—
72C2×#4082—31no—
73C2×#4081—31no—
74C2×#4081D311yescharacteristic, complemented
75C2×D4×Dic5—31no—
76C2×#4072—31no—
77C2×#4070—31no—
78#65937—316no—
79C2×#4034—31no—
80C2×#4033—31no—
81C2×#4025—31no—
82C2×#4025—31no—
83C2×#4024—31no—
84C2×#4024—31no—
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
88C2×C3×C5×D4—42no—
89C2×C3×C5×D4C2314yes—
90C22×C3×C4×C5C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C2×Dic30—42no—
96C2×Dic30C2314yes—
97C2×C5×#67—24no—
98C2×C5×#67—42no—
99C2×C5×#67C2314yes—
100C2×C5×#67C2314yes—
101C22×C5×Dic3—24no—
102C22×C5×Dic3C2311yescharacteristic
103C22×C5×Dic3C2311yescharacteristic
104C22×C5×Dic3C2314yes—
105C22×C5×Dic3C2311yescharacteristic
106C22×C3×Dic5—42no—
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C22×C3×Dic5C2311yescharacteristic
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2314yes—
112C2×#1204—24no—
113C2×#1204—42no—
114C2×#1204C2314yes—
115C2×#1204C2314yes—
116C2×D3×Dic5—42no—
117C2×D3×Dic5C2314yes—
118#6719C2314yes—
119#6719C2314yes—
120#6719C2314yes—
121#6719C2314yes—
122C4×Dic15C2314yes—
123C5×#217C2314yes—
124C5×(C2×D3)⋊C4C2314yes—
125C5×Dic3⋊C4C2314yes—
126C3×C22⋊Dic5C2314yes—
127C3×C22⋊Dic5C2314yes—
128C3×C22⋊Dic5C2314yes—
129C3×#683C2314yes—
130C3×#683C2314yes—
131Dic3⋊Dic5C2314yes—
132Dic3⋊Dic5C2314yes—
133Dic3⋊Dic5C2314yes—
134#6669C2314yes—
135#6669C2314yes—
136#6668C2314yes—
137#6668C2314yes—
138(C2×D3)⋊Dic5C2314yes—
139(C2×D3)⋊Dic5C2314yes—
140(C2×D3)⋊Dic5C2314yes—
141Dic3×Dic5C2314yes—
142Dic3×Dic5C2314yes—
143Dic3×Dic5C2314yes—
144C2×C3×#123—51no—
145C2×#939D511yescharacteristic
146C2×#936—51no—
147C2×C4×#67—51no—
148C2×#924—51no—
149#5662—516no—
150C2×#898—51no—
151C2×#896—51no—
152C2×#888—51no—
153C2×#887—51no—
154C2×#885—51no—
155C2×#885—51no—
156C2×#883—51no—
157C2×#879—51no—
158C2×#878—51no—
159C2×#877—51no—
160C22×C5×D4—31no—
161C22×C5×D4—31no—
162C22×C5×D4C2×D311yescharacteristic
163C23×C4×C5—31no—
164C23×Dic5—31no—
165C23×Dic5C2×D311yescharacteristic
166C22×Dic10—31no—
167C22×Dic10—31no—
168C22×Dic10—31no—
169C5×#121—38no—
170C2×C5×C4⋊C4—31no—
171C2×C5×C22⋊C4—31no—
172C2×C5×C22⋊C4—31no—
173C2×C22⋊Dic5—31no—
174C2×C22⋊Dic5—31no—
175C2×C22⋊Dic5—31no—
176C2×C22⋊Dic5—31no—
177C2×C22⋊Dic5—31no—
178C2×C22⋊Dic5—31no—
179C2×C22⋊Dic5—31no—
180C2×C22⋊Dic5C2×D311yescharacteristic
181C2×C22⋊Dic5C2×D311yescharacteristic
182C2×C22⋊Dic5C2×D311yescharacteristic
183#4082—38no—
184#4082—38no—
185#4082—38no—
186#4081—38no—
187#4081C2×D318yescomplemented
188D4×Dic5—38no—
189#4072—38no—
190C2×C4⋊Dic5—31no—
191C2×C4⋊Dic5—31no—
192C2×C4⋊Dic5—31no—
193#4070—38no—
194C2×#683—31no—
195C2×#683—31no—
196C2×#683—31no—
197C2×#683—31no—
198C2×#683C2×D311yescharacteristic
199C2×#683C2×D311yescharacteristic
200C2×C4×Dic5—31no—
201C2×C4×Dic5—31no—
202C2×C4×Dic5—31no—
203C2×C4×Dic5—31no—
204#4034—38no—
205#4033—38no—
206#4025—38no—
207#4025—38no—
208#4024—38no—
209#4024—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×C5×D3—22no—
221C22×C5×D3—22no—
222C22×C5×D3—22no—
223C22×C5×D3C2412yes—
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×Dic15C2412yes—
232C2×Dic15C2412yes—
233C2×Dic15C2412yes—
234C2×Dic15C2412yes—
235Dic30—44no—
236C5×#67—28no—
237C5×#67—44no—
238C2×C5×Dic3—22no—
239C2×C5×Dic3—22no—
240C2×C5×Dic3—28no—
241C2×C5×Dic3#4114yes—
242C2×C5×Dic3C2412yes—
243C2×C5×Dic3C2412yes—
244C2×C5×Dic3C2412yes—
245C2×C3×Dic5—22no—
246C2×C3×Dic5—22no—
247C2×C3×Dic5—22no—
248C2×C3×Dic5—22no—
249C2×C3×Dic5—44no—
250C2×C3×Dic5C2412yes—
251C2×C3×Dic5C2412yes—
252C2×C3×Dic5C2412yes—
253C2×C3×Dic5C2412yes—
254#1204—28no—
255#1204—44no—
256D3×Dic5—44no—
257C22×C3×D4C2×D511yescharacteristic
258C23×C3×C4—51no—
259C22×#67C2×D511yescharacteristic
260C22×#67C2×D511yescharacteristic
261C23×Dic3C2×D511yescharacteristic
262C22×C4×D3—51no—
263C22×Dic6—51no—
264C22×Dic6—51no—
265C22×Dic6—51no—
266C3×#123—58no—
267C2×C3×C4⋊C4—51no—
268C2×C3×C4⋊C4—51no—
269C2×C3×C22⋊C4—51no—
270C2×C3×C22⋊C4—51no—
271C2×C3×C22⋊C4—51no—
272C2×#217—51no—
273C2×#217—51no—
274C2×#217—51no—
275C2×#217—51no—
276C2×#217C2×D511yescharacteristic
277#939C2×D518yes—
278#936—58no—
279C4×#67—58no—
280C2×(C2×D3)⋊C4—51no—
281C2×(C2×D3)⋊C4—51no—
282C2×(C2×D3)⋊C4—51no—
283C2×(C2×D3)⋊C4C2×D511yescharacteristic
284C2×C4⋊Dic3—51no—
285C2×C4⋊Dic3—51no—
286#924—58no—
287C2×Dic3⋊C4—51no—
288C2×Dic3⋊C4—51no—
289C2×Dic3⋊C4—51no—
290C2×Dic3⋊C4—51no—
291C2×Dic3⋊C4—51no—
292C2×Dic3⋊C4C2×D511yescharacteristic
293C2×C4×Dic3—51no—
294C2×C4×Dic3—51no—
295C2×C4×Dic3—51no—
296C2×C4×Dic3—51no—
297#898—58no—
298#896—58no—
299#888—58no—
300#887—58no—
301#885—58no—
302#885—58no—
303#883—58no—
304#879—58no—
305#878—58no—
306#877—58no—
307C24×C5—31no—
308C24×C5C22×D311yescharacteristic
309C24×C5C22×D311yescharacteristic
310C2×C5×D4—34no—
311C2×C5×D4—34no—
312C2×C5×D4—42no—
313C2×C5×D4—64no—
314C2×C5×D4—122no—
315C2×C5×D4C22×D314yes—
316C22×C4×C5—31no—
317C22×C4×C5—31no—
318C22×C4×C5—31no—
319C22×C4×C5—34no—
320C22×C4×C5—64no—
321C22×C4×C5C22×D311yescharacteristic
322C22×Dic5—31no—
323C22×Dic5—31no—
324C22×Dic5—31no—
325C22×Dic5—31no—
326C22×Dic5—34no—
327C22×Dic5—42no—
328C22×Dic5—122no—
329C22×Dic5C22×D311yescharacteristic
330C22×Dic5C22×D311yescharacteristic
331C22×Dic5C22×D311yescharacteristic
332C22×Dic5C22×D311yescharacteristic
333C22×Dic5C22×D314yes—
334C2×Dic10—34no—
335C2×Dic10—34no—
336C2×Dic10—34no—
337C2×Dic10—64no—
338C2×Dic10—122no—
339C2×Dic10—122no—
340C5×C4⋊C4—34no—
341C5×C22⋊C4—34no—
342C5×C22⋊C4—34no—
343C22⋊Dic5—34no—
344C22⋊Dic5—34no—
345C22⋊Dic5—34no—
346C22⋊Dic5—34no—
347C22⋊Dic5—34no—
348C22⋊Dic5—34no—
349C22⋊Dic5—34no—
350C22⋊Dic5C22×D314yes—
351C22⋊Dic5C22×D314yes—
352C22⋊Dic5C22×D314yes—
353C4⋊Dic5—34no—
354C4⋊Dic5—34no—
355C4⋊Dic5—34no—
356#683—34no—
357#683—34no—
358#683—34no—
359#683—34no—
360#683C22×D314yes—
361#683C22×D314yes—
362C4×Dic5—34no—
363C4×Dic5—34no—
364C4×Dic5—34no—
365C4×Dic5—34no—
366#542—1516no—
367C2×C4⋊Q8—151no—
368C2×#126—151no—
369C2×#126—151no—
370C2×#124—151no—
371C2×#124—151no—
372C2×#124—151no—
373C2×#123—51no—
374C2×#123—151no—
375C2×C22⋊Q8—151no—
376C2×C22⋊Q8—151no—
377C2×C22⋊Q8—151no—
378C2×#121—31no—
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×C5×D3—22no—
395C2×C5×D3—22no—
396C2×C5×D3—22no—
397C2×C5×D3—44no—
398C3×C4×C5—22no—
399Dic15—22no—
400Dic15—22no—
401Dic15—22no—
402Dic15—22no—
403C3×Dic5—22no—
404C3×Dic5—22no—
405C3×Dic5—22no—
406C3×Dic5—22no—
407C5×Dic3—22no—
408C5×Dic3—22no—
409C5×Dic3C2×#4114yes—
410C24×C3C22×D511yescharacteristic
411C24×C3C22×D511yescharacteristic
412C23×D3C22×D511yescharacteristic
413C2×C3×D4—42no—
414C2×C3×D4C22×D514yes—
415C22×C3×C4—51no—
416C22×C3×C4—51no—
417C22×C3×C4—51no—
418C22×C3×C4—51no—
419C22×C3×C4—54no—
420C22×C3×C4—202no—
421C22×C3×C4C22×D511yescharacteristic
422C2×#67—24no—
423C2×#67—42no—
424C2×#67C22×D514yes—
425C2×#67C22×D514yes—
426C22×Dic3—24no—
427C22×Dic3—51no—
428C22×Dic3—51no—
429C22×Dic3—51no—
430C22×Dic3—51no—
431C22×Dic3C22×D514yes—
432C22×Dic3C22×D511yescharacteristic
433C22×Dic3C22×D511yescharacteristic
434C22×Dic3C22×D511yescharacteristic
435C2×C4×D3—54no—
436C2×C4×D3—202no—
437C2×Dic6—54no—
438C2×Dic6—54no—
439C2×Dic6—54no—
440C2×Dic6—104no—
441C2×Dic6—202no—
442C2×Dic6—202no—
443C3×C4⋊C4—54no—
444C3×C4⋊C4—54no—
445C3×C22⋊C4—54no—
446C3×C22⋊C4—54no—
447C3×C22⋊C4—54no—
448#217—54no—
449#217—54no—
450#217—54no—
451#217—54no—
452#217C22×D514yes—
453(C2×D3)⋊C4—54no—
454(C2×D3)⋊C4—54no—
455(C2×D3)⋊C4—54no—
456(C2×D3)⋊C4C22×D514yes—
457C4⋊Dic3—54no—
458C4⋊Dic3—54no—
459Dic3⋊C4—54no—
460Dic3⋊C4—54no—
461Dic3⋊C4—54no—
462Dic3⋊C4—54no—
463Dic3⋊C4—54no—
464Dic3⋊C4C22×D514yes—
465C4×Dic3—54no—
466C4×Dic3—54no—
467C4×Dic3—54no—
468C4×Dic3—54no—
469C23×C5—22no—
470C23×C5—22no—
471C23×C5—22no—
472C23×C5—22no—
473C23×C5—22no—
474C23×C5—22no—
475C23×C5—32no—
476C23×C5—62no—
477C23×C5—62no—
478C23×C5—62no—
479C23×C5C23×D312yes—
480C23×C5C23×D312yes—
481C23×C5C23×D311yescharacteristic
482C5×D4—44no—
483C5×D4—68no—
484C5×D4—124no—
485C2×C4×C5—22no—
486C2×C4×C5—34no—
487C2×C4×C5—32no—
488C2×C4×C5—32no—
489C2×C4×C5—32no—
490C2×C4×C5—68no—
491C2×C4×C5—62no—
492C2×C4×C5—62no—
493C2×C4×C5C23×D312yes—
494C2×Dic5—22no—
495C2×Dic5—22no—
496C2×Dic5—22no—
497C2×Dic5—22no—
498C2×Dic5—32no—
499C2×Dic5—32no—
500C2×Dic5—32no—
501C2×Dic5—32no—
502C2×Dic5—44no—
503C2×Dic5—62no—
504C2×Dic5—62no—
505C2×Dic5—62no—
506C2×Dic5—62no—
507C2×Dic5—124no—
508C2×Dic5C23×D312yes—
509C2×Dic5C23×D312yes—
510C2×Dic5C23×D312yes—
511C2×Dic5C23×D312yes—
512Dic10—68no—
513Dic10—124no—
514Dic10—124no—
515C22×Q8—151no—
516C22×Q8—151no—
517C22×Q8—151no—
518C22×D4—31no—
519C22×D4—31no—
520C22×D4D3×D511yescharacteristic
521C23×C4—31no—
522C23×C4—51no—
523C23×C4—151no—
524C4⋊Q8—158no—
525#126—158no—
526#126—158no—
527#124—158no—
528#124—158no—
529#124—158no—
530#123—58no—
531#123—158no—
532C22⋊Q8—158no—
533C22⋊Q8—158no—
534C22⋊Q8—158no—
535#121—38no—
536C4×Q8—158no—
537C4×D4—158no—
538#117—158no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—51no—
541C2×C4⋊C4—51no—
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—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×C42—151no—
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
571C5×D3—42no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—22no—
576C23×C3—22no—
577C23×C3—22no—
578C23×C3C23×D512yes—
579C23×C3C23×D512yes—
580C23×C3C23×D511yescharacteristic
581C22×D3—22no—
582C22×D3—22no—
583C22×D3—22no—
584C22×D3C23×D512yes—
585C3×D4—44no—
586C2×C3×C4—22no—
587C2×C3×C4—52no—
588C2×C3×C4—52no—
589C2×C3×C4—52no—
590C2×C3×C4—52no—
591C2×C3×C4—102no—
592C2×C3×C4—102no—
593C2×C3×C4—102no—
594C2×C3×C4—102no—
595C2×C3×C4—204no—
596C2×C3×C4C23×D512yes—
597#67—28no—
598#67—44no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—28no—
602C2×Dic3—52no—
603C2×Dic3—52no—
604C2×Dic3—52no—
605C2×Dic3—52no—
606C2×Dic3—102no—
607C2×Dic3—102no—
608C2×Dic3—102no—
609C2×Dic3—102no—
610C2×Dic3#71114yes—
611C2×Dic3C23×D512yes—
612C2×Dic3C23×D512yes—
613C2×Dic3C23×D512yes—
614C4×D3—204no—
615Dic6—108no—
616Dic6—204no—
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×C5—62no—
627C22×C5—62no—
628C22×C5—62no—
629C22×C5—124no—
630C22×C5#100412yes—
631C22×C5D3×#4112yes—
632C22×C5#101012yes—
633C22×C5C24×D311yescharacteristic
634C4×C5—22no—
635C4×C5—34no—
636C4×C5—62no—
637C4×C5—62no—
638Dic5—22no—
639Dic5—22no—
640Dic5—22no—
641Dic5—22no—
642Dic5—62no—
643Dic5—62no—
644Dic5—62no—
645Dic5—62no—
646C24—31no—
647C24C2×D3×D511yescharacteristic
648C24C2×D3×D511yescharacteristic
649C2×Q8—154no—
650C2×Q8—154no—
651C2×Q8—154no—
652C2×Q8—304no—
653C2×Q8—602no—
654C2×Q8—602no—
655C2×D4—34no—
656C2×D4—34no—
657C2×D4—42no—
658C2×D4—64no—
659C2×D4—122no—
660C2×D4C2×D3×D514yes—
661C22×C4—31no—
662C22×C4—34no—
663C22×C4—31no—
664C22×C4—31no—
665C22×C4—51no—
666C22×C4—51no—
667C22×C4—51no—
668C22×C4—51no—
669C22×C4—54no—
670C22×C4—64no—
671C22×C4—154no—
672C22×C4—151no—
673C22×C4—151no—
674C22×C4—151no—
675C22×C4—151no—
676C22×C4—202no—
677C22×C4—602no—
678C22×C4C2×D3×D511yescharacteristic
679C4⋊C4—34no—
680C4⋊C4—54no—
681C4⋊C4—54no—
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—54no—
692C22⋊C4—54no—
693C22⋊C4—54no—
694C22⋊C4—154no—
695C22⋊C4—154no—
696C22⋊C4—154no—
697C22⋊C4—154no—
698C22⋊C4—154no—
699C22⋊C4—154no—
700C22⋊C4—154no—
701C42—154no—
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×C3C2×#71112yes—
715C22×C3#414412yes—
716C22×C3#415012yes—
717C22×C3C24×D511yescharacteristic
718C2×D3—22no—
719C2×D3—22no—
720C2×D3—22no—
721C2×D3—44no—
722C3×C4—22no—
723C3×C4—102no—
724C3×C4—102no—
725C3×C4—102no—
726C3×C4—102no—
727Dic3—22no—
728Dic3—22no—
729Dic3—102no—
730Dic3—102no—
731Dic3—102no—
732Dic3—102no—
733Dic3C2×#71114yes—
734C2×C5—42no—
735C2×C5—42no—
736C2×C5—122no—
737C2×C5#566214yescomplemented
738C2×C5C2×#100411yescharacteristic
739C2×C5C2×D3×#4111yescharacteristic
740C2×C5C2×#101011yescharacteristic
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—32no—
748C23—62no—
749C23—62no—
750C23—62no—
751C23C22×D3×D512yes—
752C23C22×D3×D512yes—
753C23C22×D3×D511yescharacteristic
754Q8—308no—
755Q8—604no—
756Q8—604no—
757D4—44no—
758D4—68no—
759D4—124no—
760C2×C4—22no—
761C2×C4—34no—
762C2×C4—32no—
763C2×C4—32no—
764C2×C4—32no—
765C2×C4—52no—
766C2×C4—52no—
767C2×C4—52no—
768C2×C4—52no—
769C2×C4—68no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—102no—
773C2×C4—102no—
774C2×C4—102no—
775C2×C4—102no—
776C2×C4—152no—
777C2×C4—152no—
778C2×C4—152no—
779C2×C4—152no—
780C2×C4—204no—
781C2×C4—302no—
782C2×C4—302no—
783C2×C4—302no—
784C2×C4—302no—
785C2×C4—604no—
786C2×C4C22×D3×D512yes—
787C2×C3—42no—
788C2×C3—42no—
789C2×C3#6593714yescomplemented
790C2×C3C22×#71111yescharacteristic
791C2×C3C2×#414411yescharacteristic
792C2×C3C2×#415011yescharacteristic
793D3—42no—
794C5C2×#566211yescharacteristic, complemented, Sylow
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—44no—
802C22—44no—
803C22—62no—
804C22—62no—
805C22—62no—
806C22—124no—
807C22#9202012yes—
808C22D3×#71112yes—
809C22#9204912yes—
810C22C23×D3×D511yescharacteristic
811C4—22no—
812C4—34no—
813C4—62no—
814C4—62no—
815C4—102no—
816C4—102no—
817C4—102no—
818C4—102no—
819C4—302no—
820C4—302no—
821C4—302no—
822C4—302no—
823C3C2×#6593711yescharacteristic, complemented, Sylow
824C2—42no—
825C2—42no—
826C2—122no—
827C2#1175489014yesdirect product factor
828C2C2×#9202011yescharacteristic
829C2C2×D3×#71111yescharacteristic
830C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
prime radicalC2×C5×#939C2
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×#91825C2semidirect
3. C2×C3×#4081C2semidirect
4. C2×#91575C2semidirect
5. C2×#91574C2semidirect
6. C2×#91555C2semidirect
7. C2×Dic5×#67C2semidirect
8. C2×#91531C2semidirect
9. C2×#91529C2semidirect
10. C2×#91525C2semidirect
11. C2×#91525C2semidirect
12. #11754890C2direct (N × H)
13. C2×#91432C2semidirect
14. C2×#91367C2semidirect
15. C2×#91328C2semidirect
16. C2×#91325C2semidirect
31. #91825C22semidirect
40. C3×#4081C22semidirect
43. #91575C22semidirect
44. #91574C22semidirect
45. #91555C22semidirect
46. Dic5×#67C22semidirect
57. #91531C22semidirect
58. #91529C22semidirect
62. #91525C22semidirect
63. #91525C22semidirect
64. #91432C22semidirect
65. #91367C22semidirect
66. #91328C22semidirect
67. #91325C22semidirect
74. C2×#4081D3semidirect
187. #4081C2×D3semidirect
567. C2×C3×C5#542semidirect
705. C3×C5C2×#542semidirect
737. C2×C5#5662semidirect
789. C2×C3#65937semidirect
794. C5C2×#5662semidirect
823. C3C2×#65937semidirect
827. C2#11754890direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918252
C2×C5×#9392
C2×C3×#40812
C2×#915752
C2×#915742
C2×#915552
C2×Dic5×#672
C2×#915312
C2×#915292
C2×#915252
#117548902
C2×#914322
C2×#913672
C2×#913282
C2×#913252
C2×#659373
C2×#56625