Finite Group Databasebeta

← C2×#11753343 #14481451

Subgroups — C2×#11753343 #14481451

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×#91785C211yesmaximal, characteristic, complemented
2C2×C5×#894C211yesmaximal, characteristic, complemented
3C2×C3×#4033C211yesmaximal, characteristic, complemented
4C2×C4×#1203C211yesmaximal, characteristic, complemented
5C2×#91416C211yesmaximal, characteristic
6C2×#91410C211yesmaximal, characteristic, complemented
7C2×#91398C211yesmaximal, characteristic, complemented
8C2×#91387C211yesmaximal, characteristic, complemented
9C2×#91373C211yesmaximal, characteristic, complemented
10C2×#91372C211yesmaximal, characteristic, complemented
11C2×#91355C211yesmaximal, characteristic, complemented
12C2×#91352C211yesmaximal, characteristic, complemented
13C2×#91350C211yesmaximal, characteristic, complemented
14C2×#91328C211yesmaximal, characteristic, complemented
15C2×#91326C211yesmaximal, characteristic, complemented
16#11753343C2116yesmaximal, direct product factor
17C2×#65996—31nomaximal, Hall
18C22×C4×D15C2211yescharacteristic
19C22×Dic30C2211yescharacteristic
20C22×C5×D12C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic
22C22×C3×Dic10C2211yescharacteristic
23C22×#1204C2211yescharacteristic
24C22×#1203C2211yescharacteristic
25C22×#1203C2211yescharacteristic
26C22×D3×Dic5C2211yescharacteristic
27C2×C3×C5×C4⋊C4C2211yescharacteristic
28C2×#6714C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×#6712C2211yescharacteristic
31C2×#6712C2211yescharacteristic
32#91785C2218yescomplemented
33C2×C5×(C2×D3)⋊C4C2211yescharacteristic
34C2×C5×(C2×D3)⋊C4C2211yescharacteristic
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic
36C2×C5×Dic3⋊C4C2211yescharacteristic
37C5×#894C2218yescomplemented
38C2×C3×#683C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic
40C2×C3×C4×Dic5C2211yescharacteristic
41C2×C3×C4×Dic5C2211yescharacteristic
42C2×C3×C4×Dic5C2211yescharacteristic
43C3×#4033C2218yescomplemented
44C2×Dic3⋊Dic5C2211yescharacteristic
45C2×Dic3⋊Dic5C2211yescharacteristic
46C2×#6669C2211yescharacteristic
47C2×#6668C2211yescharacteristic
48C2×#6667C2211yescharacteristic
49C2×#6667C2211yescharacteristic
50C2×(C2×D3)⋊Dic5C2211yescharacteristic
51C2×(C2×D3)⋊Dic5C2211yescharacteristic
52C2×(C2×D3)⋊Dic5C2211yescharacteristic
53C2×(C2×D3)⋊Dic5C2211yescharacteristic
54C2×(C2×D3)⋊Dic5C2211yescharacteristic
55C2×Dic3×Dic5C2211yescharacteristic
56C4×#1203C2218yescomplemented
57#91416C2218yes—
58#91410C2218yescomplemented
59#91398C2218yescomplemented
60#91387C2218yescomplemented
61#91373C2218yescomplemented
62#91372C2218yescomplemented
63#91355C2218yescomplemented
64#91352C2218yescomplemented
65#91350C2218yescomplemented
66#91328C2218yescomplemented
67#91326C2218yescomplemented
68C2×#5582—51nomaximal, Hall
69C2×C5×#123—31no—
70C2×#4085—31no—
71C2×#4082—31no—
72C2×C4×C22⋊D5—31no—
73C2×#4070—31no—
74#65996—316no—
75C2×#4044—31no—
76C2×#4042—31no—
77C2×#4034—31no—
78C2×#4033D311yescharacteristic, complemented
79C2×#4031—31no—
80C2×#4031—31no—
81C2×#4029—31no—
82C2×#4025—31no—
83C2×#4024—31no—
84C2×#4023—31no—
85C23×D15C2311yescharacteristic
86C23×C5×D3C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
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—
96C2×Dic30—42no—
97C2×Dic30C2314yes—
98C22×C5×Dic3C2311yescharacteristic
99C22×C5×Dic3C2311yescharacteristic
100C2×C5×D12—42no—
101C2×C5×D12C2314yes—
102C2×C4×C5×D3—42no—
103C2×C4×C5×D3C2314yes—
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C2×C3×Dic10—24no—
109C2×C3×Dic10C2314yes—
110C2×#1204—42no—
111C2×#1204C2314yes—
112C2×#1203—24no—
113C2×#1203—42no—
114C2×#1203C2314yes—
115C2×#1203C2314yes—
116C2×D3×Dic5—24no—
117C2×D3×Dic5C2314yes—
118C3×C5×C4⋊C4C2314yes—
119#6714C2314yes—
120#6714C2314yes—
121#6712C2314yes—
122#6712C2314yes—
123C5×(C2×D3)⋊C4C2314yes—
124C5×(C2×D3)⋊C4C2314yes—
125C5×(C2×D3)⋊C4C2314yes—
126C5×Dic3⋊C4C2314yes—
127C3×#683C2314yes—
128C3×#683C2314yes—
129C3×C4×Dic5C2314yes—
130C3×C4×Dic5C2314yes—
131C3×C4×Dic5C2314yes—
132Dic3⋊Dic5C2314yes—
133Dic3⋊Dic5C2314yes—
134#6669C2314yes—
135#6668C2314yes—
136#6667C2314yes—
137#6667C2314yes—
138(C2×D3)⋊Dic5C2314yes—
139(C2×D3)⋊Dic5C2314yes—
140(C2×D3)⋊Dic5C2314yes—
141(C2×D3)⋊Dic5C2314yes—
142(C2×D3)⋊Dic5C2314yes—
143Dic3×Dic5C2314yes—
144C2×C3×C4×Q8—51no—
145C2×#947—51no—
146C2×#946—51no—
147#5582—516no—
148C2×#896—51no—
149C2×#896—51no—
150C2×#895—51no—
151C2×#894—51no—
152C2×#894D511yescharacteristic, complemented
153C2×#888—51no—
154C2×#876—51no—
155C2×#876—51no—
156C2×#875—51no—
157C2×#875—51no—
158C2×C4×D12—51no—
159C2×#872—51no—
160C22×C5×D4—31no—
161C23×C4×C5—31no—
162C22×C22⋊D5—31no—
163C22×C22⋊D5—31no—
164C23×Dic5—31no—
165C22×C4×D5—31no—
166C22×Dic10—31no—
167C22×Dic10—31no—
168C22×Dic10C2×D311yescharacteristic
169C5×#123—38no—
170C2×C5×C4⋊C4—31no—
171C2×C5×C4⋊C4C2×D311yescharacteristic
172C2×C5×C22⋊C4—31no—
173C2×C5×C22⋊C4—31no—
174C2×C5×C22⋊C4—31no—
175C2×C22⋊Dic5—31no—
176C2×C22⋊Dic5—31no—
177C2×C22⋊Dic5—31no—
178C2×C22⋊Dic5—31no—
179C2×C22⋊Dic5—31no—
180#4085—38no—
181#4082—38no—
182C4×C22⋊D5—38no—
183C2×#685—31no—
184C2×#685—31no—
185C2×#685—31no—
186C2×#685—31no—
187C2×C4⋊Dic5—31no—
188C2×C4⋊Dic5—31no—
189#4070—38no—
190C2×#683—31no—
191C2×#683—31no—
192C2×#683—31no—
193C2×#683—31no—
194C2×#683C2×D311yescharacteristic
195C2×#683C2×D311yescharacteristic
196C2×C4×Dic5—31no—
197C2×C4×Dic5C2×D311yescharacteristic
198C2×C4×Dic5C2×D311yescharacteristic
199C2×C4×Dic5C2×D311yescharacteristic
200#4044—38no—
201#4042—38no—
202#4034—38no—
203#4033C2×D318yescomplemented
204#4031—38no—
205#4031—38no—
206#4029—38no—
207#4025—38no—
208#4024—38no—
209#4023—38no—
210C2×#542—151noSylow
211C23×C3×C5C2411yescharacteristic
212C22×D15—22no—
213C22×D15—22no—
214C22×D15—22no—
215C22×D15C2412yes—
216C22×C5×D3—22no—
217C22×C5×D3—22no—
218C22×C5×D3—22no—
219C22×C5×D3—22no—
220C22×C5×D3—22no—
221C22×C5×D3—22no—
222C22×C5×D3C2412yes—
223C22×C5×D3C2412yes—
224C2×C3×C4×C5—22no—
225C2×C3×C4×C5—22no—
226C2×C3×C4×C5—22no—
227C2×C3×C4×C5C2412yes—
228C2×C3×C4×C5C2412yes—
229C2×C3×C4×C5C2412yes—
230C2×Dic15—22no—
231C2×Dic15—22no—
232C2×Dic15—22no—
233C2×Dic15C2412yes—
234C2×Dic15C2412yes—
235C2×Dic15C2412yes—
236C4×D15—44no—
237Dic30—44no—
238C2×C5×Dic3—22no—
239C2×C5×Dic3—22no—
240C2×C5×Dic3C2412yes—
241C2×C5×Dic3C2412yes—
242C5×D12—44no—
243C4×C5×D3—44no—
244C2×C3×Dic5—22no—
245C2×C3×Dic5—22no—
246C2×C3×Dic5—22no—
247C2×C3×Dic5#4114yes—
248C2×C3×Dic5C2412yes—
249C2×C3×Dic5C2412yes—
250C2×C3×Dic5C2412yes—
251C2×C3×Dic5C2412yes—
252C3×Dic10—28no—
253#1204—44no—
254#1203—28no—
255#1203—44no—
256D3×Dic5—28no—
257C22×C3×Q8—51no—
258C22×D12—51no—
259C22×D12—51no—
260C22×D12C2×D511yescharacteristic
261C22×C4×D3—51no—
262C22×C4×D3—51no—
263C22×C4×D3C2×D511yescharacteristic
264C22×Dic6—51no—
265C22×Dic6—51no—
266C3×C4×Q8—58no—
267C2×C3×C4⋊C4—51no—
268C2×C3×C4⋊C4—51no—
269C2×C3×C4⋊C4C2×D511yescharacteristic
270C2×C3×C42—51no—
271C2×C3×C42—51no—
272C2×C3×C42—51no—
273#947—58no—
274#946—58no—
275C2×(C2×D3)⋊C4—51no—
276C2×(C2×D3)⋊C4—51no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4—51no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4—51no—
281C2×(C2×D3)⋊C4—51no—
282C2×(C2×D3)⋊C4—51no—
283C2×(C2×D3)⋊C4—51no—
284C2×(C2×D3)⋊C4C2×D511yescharacteristic
285C2×(C2×D3)⋊C4C2×D511yescharacteristic
286C2×(C2×D3)⋊C4C2×D511yescharacteristic
287C2×C4⋊Dic3—51no—
288C2×Dic3⋊C4—51no—
289C2×Dic3⋊C4—51no—
290C2×Dic3⋊C4—51no—
291C2×Dic3⋊C4—51no—
292C2×Dic3⋊C4—51no—
293C2×Dic3⋊C4C2×D511yescharacteristic
294C2×C4×Dic3—51no—
295#896—58no—
296#896—58no—
297#895—58no—
298#894—58no—
299#894C2×D518yescomplemented
300#888—58no—
301#876—58no—
302#876—58no—
303#875—58no—
304#875—58no—
305C4×D12—58no—
306#872—58no—
307C24×C5—31no—
308C24×C5—31no—
309C23×D5—31no—
310C2×C5×D4—34no—
311C2×C5×D4—122no—
312C22×C4×C5—31no—
313C22×C4×C5—31no—
314C22×C4×C5—34no—
315C22×C4×C5—122no—
316C22×C4×C5C22×D311yescharacteristic
317C22×C4×C5C22×D311yescharacteristic
318C22×C4×C5C22×D311yescharacteristic
319C2×C22⋊D5—34no—
320C2×C22⋊D5—34no—
321C2×C22⋊D5—64no—
322C2×C22⋊D5—122no—
323C22×Dic5—31no—
324C22×Dic5—31no—
325C22×Dic5—31no—
326C22×Dic5—34no—
327C22×Dic5—64no—
328C22×Dic5C22×D311yescharacteristic
329C22×Dic5C22×D311yescharacteristic
330C22×Dic5C22×D311yescharacteristic
331C22×Dic5C22×D311yescharacteristic
332C2×C4×D5—34no—
333C2×C4×D5—122no—
334C2×Dic10—24no—
335C2×Dic10—34no—
336C2×Dic10—34no—
337C2×Dic10—122no—
338C2×Dic10—122no—
339C2×Dic10C22×D314yes—
340C5×C4⋊C4—34no—
341C5×C4⋊C4C22×D314yes—
342C5×C22⋊C4—34no—
343C5×C22⋊C4—34no—
344C5×C22⋊C4—34no—
345C22⋊Dic5—34no—
346C22⋊Dic5—34no—
347C22⋊Dic5—34no—
348C22⋊Dic5—34no—
349C22⋊Dic5—34no—
350#685—34no—
351#685—34no—
352#685—34no—
353#685—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×Dic5C22×D314yes—
364C4×Dic5C22×D314yes—
365C4×Dic5C22×D314yes—
366#542—1516no—
367C2×C4⋊Q8—151no—
368C2×#126—151no—
369C2×#126—151no—
370C2×#124—151no—
371C2×#124—151no—
372C2×#124—151no—
373C2×#123—31no—
374C2×#123—151no—
375C2×C22⋊Q8—151no—
376C2×C22⋊Q8—151no—
377C2×C22⋊Q8—151no—
378C2×#121—151no—
379C2×C4×Q8—51no—
380C2×C4×D4—151no—
381C2×#117—151no—
382C22×C3×C5C2×#4112yes—
383C22×C3×C5H(5,𝔽2)12yes—
384C22×C3×C52−1+412yes—
385C22×C3×C5C2511yescharacteristic
386C2×D15—22no—
387C2×D15—22no—
388C2×D15—22no—
389C2×D15—44no—
390C2×C5×D3—22no—
391C2×C5×D3—22no—
392C2×C5×D3—22no—
393C2×C5×D3—22no—
394C2×C5×D3—22no—
395C2×C5×D3—22no—
396C2×C5×D3—44no—
397C2×C5×D3—44no—
398C3×C4×C5—22no—
399C3×C4×C5—22no—
400C3×C4×C5—22no—
401Dic15—22no—
402Dic15—22no—
403Dic15—22no—
404C3×Dic5—22no—
405C3×Dic5—22no—
406C3×Dic5—22no—
407C3×Dic5C2×#4114yes—
408C5×Dic3—22no—
409C5×Dic3—22no—
410C23×D3—51no—
411C23×D3C22×D511yescharacteristic
412C23×D3C22×D511yescharacteristic
413C2×C3×Q8—54no—
414C2×C3×Q8—104no—
415C22×C3×C4—51no—
416C22×C3×C4—51no—
417C22×C3×C4—51no—
418C22×C3×C4—51no—
419C22×C3×C4C22×D511yescharacteristic
420C22×C3×C4C22×D511yescharacteristic
421C22×C3×C4C22×D511yescharacteristic
422C22×Dic3—51no—
423C22×Dic3—51no—
424C22×Dic3—51no—
425C22×Dic3C22×D511yescharacteristic
426C22×Dic3C22×D511yescharacteristic
427C2×D12—42no—
428C2×D12—54no—
429C2×D12—54no—
430C2×D12—104no—
431C2×D12—202no—
432C2×D12C22×D514yes—
433C2×C4×D3—42no—
434C2×C4×D3—54no—
435C2×C4×D3—54no—
436C2×C4×D3—104no—
437C2×C4×D3—202no—
438C2×C4×D3C22×D514yes—
439C2×Dic6—54no—
440C2×Dic6—54no—
441C2×Dic6—202no—
442C2×Dic6—202no—
443C3×C4⋊C4—54no—
444C3×C4⋊C4—54no—
445C3×C4⋊C4C22×D514yes—
446C3×C42—54no—
447C3×C42—54no—
448C3×C42—54no—
449(C2×D3)⋊C4—54no—
450(C2×D3)⋊C4—54no—
451(C2×D3)⋊C4—54no—
452(C2×D3)⋊C4—54no—
453(C2×D3)⋊C4—54no—
454(C2×D3)⋊C4—54no—
455(C2×D3)⋊C4—54no—
456(C2×D3)⋊C4—54no—
457(C2×D3)⋊C4—54no—
458(C2×D3)⋊C4C22×D514yes—
459(C2×D3)⋊C4C22×D514yes—
460(C2×D3)⋊C4C22×D514yes—
461C4⋊Dic3—54no—
462Dic3⋊C4—54no—
463Dic3⋊C4—54no—
464Dic3⋊C4—54no—
465Dic3⋊C4—54no—
466Dic3⋊C4—54no—
467Dic3⋊C4C22×D514yes—
468C4×Dic3—54no—
469C23×C5—32no—
470C23×C5—32no—
471C23×C5—62no—
472C23×C5—62no—
473C23×C5—62no—
474C23×C5—62no—
475C23×C5—62no—
476C23×C5—62no—
477C23×C5C23×D311yescharacteristic
478C22×D5—32no—
479C22×D5—62no—
480C22×D5—62no—
481C22×D5—62no—
482C5×D4—124no—
483C2×C4×C5—22no—
484C2×C4×C5—22no—
485C2×C4×C5—22no—
486C2×C4×C5—32no—
487C2×C4×C5—32no—
488C2×C4×C5—62no—
489C2×C4×C5—62no—
490C2×C4×C5—124no—
491C2×C4×C5C23×D312yes—
492C2×C4×C5C23×D312yes—
493C2×C4×C5C23×D312yes—
494C22⋊D5—68no—
495C22⋊D5—124no—
496C2×Dic5—22no—
497C2×Dic5—22no—
498C2×Dic5—22no—
499C2×Dic5—32no—
500C2×Dic5—32no—
501C2×Dic5—32no—
502C2×Dic5—62no—
503C2×Dic5—62no—
504C2×Dic5—62no—
505C2×Dic5—68no—
506C2×Dic5#23514yes—
507C2×Dic5C23×D312yes—
508C2×Dic5C23×D312yes—
509C2×Dic5C23×D312yes—
510C2×Dic5C23×D312yes—
511C4×D5—124no—
512Dic10—28no—
513Dic10—124no—
514Dic10—124no—
515C22×Q8—51no—
516C22×Q8—151no—
517C22×Q8—151no—
518C22×D4—31no—
519C22×D4—151no—
520C22×D4—151no—
521C23×C4—31no—
522C23×C4—151no—
523C23×C4—151no—
524C4⋊Q8—158no—
525#126—158no—
526#126—158no—
527#124—158no—
528#124—158no—
529#124—158no—
530#123—38no—
531#123—158no—
532C22⋊Q8—158no—
533C22⋊Q8—158no—
534C22⋊Q8—158no—
535#121—158no—
536C4×Q8—58no—
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⋊C4D3×D511yescharacteristic
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—151no—
553C2×C22⋊C4—151no—
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—51no—
562C2×C42—51no—
563C2×C42—51no—
564C2×C42—151no—
565C2×C3×C5#54214yescomplemented
566C2×C3×C5C22×#4111yescharacteristic
567C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
568C2×C3×C5C2×2−1+411yescharacteristic
569D15—42no—
570C5×D3—42no—
571C5×D3—42no—
572C23×C3C23×D511yescharacteristic
573C22×D3—22no—
574C22×D3—22no—
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—52no—
580C22×D3—102no—
581C22×D3—102no—
582C22×D3—102no—
583C22×D3C23×D512yes—
584C22×D3C23×D512yes—
585C3×Q8—108no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—54no—
590C2×C3×C4—52no—
591C2×C3×C4—52no—
592C2×C3×C4—52no—
593C2×C3×C4—52no—
594C2×C3×C4—102no—
595C2×C3×C4—102no—
596C2×C3×C4—102no—
597C2×C3×C4C23×D512yes—
598C2×C3×C4C23×D512yes—
599C2×C3×C4C23×D512yes—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—52no—
603C2×Dic3—52no—
604C2×Dic3—52no—
605C2×Dic3—102no—
606C2×Dic3—102no—
607C2×Dic3—102no—
608C2×Dic3C23×D512yes—
609C2×Dic3C23×D512yes—
610D12—44no—
611D12—108no—
612D12—204no—
613C4×D3—44no—
614C4×D3—108no—
615C4×D3—204no—
616Dic6—204no—
617Dic6—204no—
618C22×C5—62no—
619C22×C5—62no—
620C22×C5—62no—
621C22×C5—62no—
622C22×C5—62no—
623C22×C5—62no—
624C22×C5—124no—
625C22×C5—124no—
626C22×C5C2×#23512yes—
627C22×C5#100712yes—
628C22×C5#100912yes—
629C22×C5C24×D311yescharacteristic
630C2×D5—62no—
631C2×D5—62no—
632C2×D5—62no—
633C2×D5—124no—
634C4×C5—22no—
635C4×C5—22no—
636C4×C5—22no—
637C4×C5—62no—
638C4×C5—62no—
639Dic5—22no—
640Dic5—22no—
641Dic5—22no—
642Dic5—62no—
643Dic5—62no—
644Dic5—62no—
645Dic5C2×#23514yes—
646C24—31no—
647C24—31no—
648C24—151no—
649C2×Q8—54no—
650C2×Q8—104no—
651C2×Q8—154no—
652C2×Q8—154no—
653C2×Q8—602no—
654C2×Q8—602no—
655C2×D4—34no—
656C2×D4—122no—
657C2×D4—154no—
658C2×D4—154no—
659C2×D4—304no—
660C2×D4—602no—
661C22×C4—31no—
662C22×C4—31no—
663C22×C4—34no—
664C22×C4—51no—
665C22×C4—51no—
666C22×C4—51no—
667C22×C4—51no—
668C22×C4—122no—
669C22×C4—154no—
670C22×C4—151no—
671C22×C4—151no—
672C22×C4—151no—
673C22×C4—154no—
674C22×C4—304no—
675C22×C4—602no—
676C22×C4C2×D3×D511yescharacteristic
677C22×C4C2×D3×D511yescharacteristic
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⋊C4C2×D3×D514yes—
689C22⋊C4—34no—
690C22⋊C4—34no—
691C22⋊C4—34no—
692C22⋊C4—154no—
693C22⋊C4—154no—
694C22⋊C4—154no—
695C22⋊C4—154no—
696C22⋊C4—154no—
697C22⋊C4—154no—
698C22⋊C4—154no—
699C22⋊C4—154no—
700C22⋊C4—154no—
701C42—54no—
702C42—54no—
703C42—54no—
704C42—154no—
705C3×C5C2×#54211yescharacteristic, complemented, Hall
706C22×C3#414412yes—
707C22×C3D5×#4112yes—
708C22×C3#415012yes—
709C22×C3C24×D511yescharacteristic
710C2×D3—22no—
711C2×D3—22no—
712C2×D3—22no—
713C2×D3—22no—
714C2×D3—22no—
715C2×D3—22no—
716C2×D3—44no—
717C2×D3—44no—
718C2×D3—102no—
719C2×D3—102no—
720C2×D3—102no—
721C2×D3—204no—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—22no—
725C3×C4—54no—
726C3×C4—102no—
727C3×C4—102no—
728C3×C4—102no—
729Dic3—22no—
730Dic3—22no—
731Dic3—102no—
732Dic3—102no—
733Dic3—102no—
734C2×C5—122no—
735C2×C5—122no—
736C2×C5#558214yescomplemented
737C2×C5C22×#23511yescharacteristic
738C2×C5C2×#100711yescharacteristic
739C2×C5C2×#100911yescharacteristic
740D5—122no—
741C23—32no—
742C23—32no—
743C23—62no—
744C23—62no—
745C23—62no—
746C23—62no—
747C23—62no—
748C23—62no—
749C23—152no—
750C23—302no—
751C23—302no—
752C23—302no—
753C23C22×D3×D511yescharacteristic
754Q8—108no—
755Q8—604no—
756Q8—604no—
757D4—124no—
758D4—308no—
759D4—604no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—32no—
764C2×C4—32no—
765C2×C4—54no—
766C2×C4—52no—
767C2×C4—52no—
768C2×C4—52no—
769C2×C4—52no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—102no—
773C2×C4—102no—
774C2×C4—102no—
775C2×C4—124no—
776C2×C4—152no—
777C2×C4—152no—
778C2×C4—152no—
779C2×C4—308no—
780C2×C4—302no—
781C2×C4—302no—
782C2×C4—302no—
783C2×C4—604no—
784C2×C4C22×D3×D512yes—
785C2×C4C22×D3×D512yes—
786C2×C4C22×D3×D512yes—
787C2×C3#6599614yescomplemented
788C2×C3C2×#414411yescharacteristic
789C2×C3C2×D5×#4111yescharacteristic
790C2×C3C2×#415011yescharacteristic
791D3—42no—
792D3—42no—
793D3—202no—
794C5C2×#558211yescharacteristic, complemented, Sylow
795C22—62no—
796C22—62no—
797C22—62no—
798C22—62no—
799C22—62no—
800C22—62no—
801C22—124no—
802C22—124no—
803C22—302no—
804C22—302no—
805C22—302no—
806C22—604no—
807C22D5×#23512yes—
808C22#9202712yes—
809C22#9203012yes—
810C22C23×D3×D511yescharacteristic
811C4—22no—
812C4—22no—
813C4—22no—
814C4—54no—
815C4—62no—
816C4—62no—
817C4—102no—
818C4—102no—
819C4—102no—
820C4—302no—
821C4—302no—
822C4—302no—
823C3C2×#6599611yescharacteristic, complemented, Sylow
824C2—122no—
825C2—122no—
826C2—602no—
827C2#1175334314yesdirect product factor
828C2C2×D5×#23511yescharacteristic
829C2C2×#9202711yescharacteristic
830C2C2×#9203011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC2×#91416C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#542
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
1. C2×#91785C2semidirect
2. C2×C5×#894C2semidirect
3. C2×C3×#4033C2semidirect
4. C2×C4×#1203C2semidirect
6. C2×#91410C2semidirect
7. C2×#91398C2semidirect
8. C2×#91387C2semidirect
9. C2×#91373C2semidirect
10. C2×#91372C2semidirect
11. C2×#91355C2semidirect
12. C2×#91352C2semidirect
13. C2×#91350C2semidirect
14. C2×#91328C2semidirect
15. C2×#91326C2semidirect
16. #11753343C2direct (N × H)
32. #91785C22semidirect
37. C5×#894C22semidirect
43. C3×#4033C22semidirect
56. C4×#1203C22semidirect
58. #91410C22semidirect
59. #91398C22semidirect
60. #91387C22semidirect
61. #91373C22semidirect
62. #91372C22semidirect
63. #91355C22semidirect
64. #91352C22semidirect
65. #91350C22semidirect
66. #91328C22semidirect
67. #91326C22semidirect
78. C2×#4033D3semidirect
152. C2×#894D5semidirect
203. #4033C2×D3semidirect
299. #894C2×D5semidirect
565. C2×C3×C5#542semidirect
705. C3×C5C2×#542semidirect
736. C2×C5#5582semidirect
787. C2×C3#65996semidirect
794. C5C2×#5582semidirect
823. C3C2×#65996semidirect
827. C2#11753343direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917852
C2×C5×#8942
C2×C3×#40332
C2×C4×#12032
C2×#914162
C2×#914102
C2×#913982
C2×#913872
C2×#913732
C2×#913722
C2×#913552
C2×#913522
C2×#913502
C2×#913282
C2×#913262
#117533432
C2×#659963
C2×#55825