Finite Group Databasebeta

← #14281714

Subgroups — #14281714

Order 1920.

624 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#1200C211yesmaximal, characteristic
2#11751812C211yesmaximal, characteristic, complemented
3#11751777C211yesmaximal, characteristic, complemented
4D4⋊(C3⋊#170)C211yesmaximal, characteristic, complemented
5C3×D4⋊#170C211yesmaximal, characteristic, complemented
6#11746491C211yesmaximal, characteristic, complemented
7#11746490C211yesmaximal, characteristic, complemented
8#10604403—31nomaximal, Hall
9C2×D4×D15C411yescharacteristic
10C22×#1200—21no—
11C5×D4×Dic3C411yescharacteristic
12C3×D4×Dic5C2211yescharacteristic
13#91561—21no—
14#91556—21no—
15#91552—21no—
16#91437C411yescharacteristic
17#91428C411yescharacteristic
18#91418C2211yescharacteristic
19C4×#1200C2211yescharacteristic
20C4⋊(C3⋊#170)C2211yescharacteristic, complemented
21C4×C3⋊#170C2211yescharacteristic, complemented
22C3×C4⋊#170C2211yescharacteristic, complemented
23C3×C4×#170C2211yescharacteristic, complemented
24#91177—21no—
25#91171—21no—
26#91171—21no—
27Dic3×#170—21no—
28#68167—51nomaximal, Hall
29C4×D4×D5—31no—
30#65680—31no—
31#65678—31no—
32D4⋊#170—31no—
33D4⋊#170D311yescharacteristic, complemented
34#64871—31no—
35#64871—31no—
36C23×D15—21no—
37C2×C3×C5×D4C2×C411yescharacteristic
38C2×#1220—21no—
39D4×D15—22no—
40D4×D15C814yescomplemented
41C2×D60C2×C411yescharacteristic
42C2×C4×D15C2×C411yescharacteristic
43C22×C5×Dic3—21no—
44C22×C3×Dic5—21no—
45C2×#1200—21no—
46C2×#1200—21no—
47C2×#1200—21no—
48C2×#1200—42no—
49C2×#1200—42no—
50C2×#1200D411yescharacteristic
51C2×#1200D411yescharacteristic
52C2×C3⋊#170—21no—
53C2×C3⋊#170—21no—
54C2×C3×#170—21no—
55C2×C3×#170—21no—
56C5×#217—21no—
57C5×C4⋊Dic3C2×C411yescharacteristic
58C4×C5×Dic3C2×C411yescharacteristic
59C3×C22⋊Dic5—21no—
60C3×C4⋊Dic5C2×C411yescharacteristic
61C3×C4×Dic5C2311yescharacteristic
62#6669—21no—
63#6667—21no—
64#6667—21no—
65Dic3×Dic5D411yescharacteristic
66Dic3×Dic5D411yescharacteristic
67C4×D3×D4—51no—
68#4833—51no—
69#4685—51no—
70C3×D4⋊C8—51no—
71D4⋊(C3⋊C8)—51no—
72#4483—51no—
73#4459—51no—
74C2×D4×D5—31no—
75C22×C4×D5—61no—
76C4×C5×D4—31no—
77D4×Dic5C2×D311yescharacteristic
78C4×C22⋊D5—61no—
79#4039—31no—
80D5×C4⋊C4—31no—
81#4027—61no—
82D5×C22⋊C4—61no—
83C4×D20—31no—
84C42×D5—31no—
85#4004—61no—
86#4003—61no—
87#4003—61no—
88C4⋊#170—31no—
89C4⋊#170C2×D311yescharacteristic, complemented
90C4×#170—31no—
91C4×#170—61no—
92C4×#170C2×D311yescharacteristic, complemented
93#1478—151noSylow
94C23×C3×C5—21no—
95C22×D15—21no—
96C22×D15—24no—
97C22×D15—42no—
98C22×D15—42no—
99C22×D15C22⋊C411yescharacteristic
100C3×C5×D4—21no—
101C3×C5×D4C2×C812yes—
102C2×C3×C4×C5C22×C411yescharacteristic
103#1220—24no—
104C2×Dic15C22⋊C411yescharacteristic
105D60—21no—
106D60C2×C812yes—
107C4×D15C2×C812yes—
108C4×D15M1612yes—
109C2×C5×Dic3—21no—
110C2×C5×Dic3—42no—
111C2×C5×Dic3C22⋊C411yescharacteristic
112C2×C5×Dic3C22⋊C411yescharacteristic
113C2×C3×Dic5—21no—
114C2×C3×Dic5—41no—
115C2×C3×Dic5—41no—
116C2×C3×Dic5C2×D411yescharacteristic
117C2×C3×Dic5C2×D411yescharacteristic
118#1200—21no—
119#1200—21no—
120#1200—41no—
121#1200—42no—
122#1200—42no—
123#1200—41no—
124#1200—41no—
125C3⋊#170—41no—
126C3⋊#170—41no—
127C3×#170—41no—
128C3×#170—41no—
129C2×D3×D4—51no—
130C22×C4×D3—101no—
131C3×C4×D4—51no—
132D4×Dic3AGL(1,𝔽5)11yescharacteristic
133C4×#67—101no—
134#893—51no—
135D3×C4⋊C4—51no—
136#67⋊C4—101no—
137D3×C22⋊C4—101no—
138C4×D12—51no—
139C42×D3—51no—
140C3×C4⋊C8—51no—
141C3×C4×C8—51no—
142(C2×D3)⋊C8—101no—
143(C2×D3)⋊C8—101no—
144Dic3⋊C8—101no—
145C8×Dic3—101no—
146C4⋊(C3⋊C8)—51no—
147C4×C3⋊C8—51no—
148C23×D5—61no—
149C2×C5×D4C4×D311yescharacteristic
150C22×C4×C5—61no—
151C2×C22⋊D5—61no—
152C22×Dic5—21no—
153D4×D5—34no—
154D4×D5—62no—
155C2×D20—31no—
156C2×C4×D5—31no—
157C2×C4×D5—31no—
158C2×C4×D5—31no—
159C2×C4×D5—61no—
160C2×C4×D5—61no—
161C2×C4×D5—61no—
162C2×C4×D5—122no—
163C2×C4×D5—122no—
164C2×#170—21no—
165C2×#170—21no—
166C2×#170—61no—
167C2×#170—61no—
168C5×C4⋊C4—31no—
169C5×C22⋊C4—61no—
170C42×C5—31no—
171C22⋊Dic5—21no—
172#685—61no—
173#685—61no—
174C4⋊Dic5C4×D311yescharacteristic
175#683—61no—
176C4×Dic5—31no—
177C4×Dic5—31no—
178C4×Dic5C22×D311yescharacteristic
179C2×C4×D4—151no—
180#431—151no—
181#431—151no—
182D4⋊C8—51no—
183D4⋊C8—151no—
184D4⋊C8—151no—
185D4⋊C8—151no—
186C22×C3×C5—22no—
187C22×C3×C5—41no—
188C22×C3×C5—41no—
189C22×C3×C5C2×C22⋊C411yescharacteristic
190C2×D15—21no—
191C2×D15—21no—
192C2×D15—22no—
193C2×D15—48no—
194C2×D15—41no—
195C2×D15—41no—
196C2×D15C22⋊C812yes—
197C3×C4×C5C22×C811yescharacteristic
198C3×C4×C5C2×M1611yescharacteristic
199Dic15C22⋊C812yes—
200C3×Dic5—21no—
201C3×Dic5—41no—
202C3×Dic5AGL(1,ℤ/8)11yescharacteristic
203C3×Dic5AGL(1,ℤ/8)11yescharacteristic
204C5×Dic3—21no—
205C5×Dic3—21no—
206C5×Dic3—41no—
207C23×D3—101no—
208C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
209C22×C3×C4—101no—
210C2×#67—101no—
211C22×Dic3—21no—
212D3×D4—54no—
213D3×D4—102no—
214C2×D12—51no—
215C2×C4×D3—51no—
216C2×C4×D3—51no—
217C2×C4×D3—51no—
218C2×C4×D3—101no—
219C2×C4×D3—101no—
220C2×C4×D3—101no—
221C2×C4×D3—202no—
222C2×C4×D3—202no—
223C2×C3×C8—101no—
224C2×C3×C8—101no—
225C3×C4⋊C4—51no—
226C3×C22⋊C4—101no—
227C3×C42—51no—
228#217—21no—
229(C2×D3)⋊C4—101no—
230(C2×D3)⋊C4—101no—
231C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
232Dic3⋊C4—101no—
233C4×Dic3—51no—
234C4×Dic3—51no—
235C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
236C2×C3⋊C8—101no—
237C2×C3⋊C8—101no—
238C23×C5—21no—
239C22×D5—31no—
240C22×D5—64no—
241C22×D5—61no—
242C22×D5—122no—
243C22×D5—122no—
244C5×D4—21no—
245C5×D4D3×C812yes—
246C2×C4×C5—31no—
247C2×C4×C5—31no—
248C2×C4×C5—61no—
249C2×C4×C5—122no—
250C2×C4×C5C2×C4×D311yescharacteristic
251C22⋊D5—64no—
252C2×Dic5—21no—
253C2×Dic5—31no—
254C2×Dic5—41no—
255C2×Dic5—41no—
256C2×Dic5D3×D411yescharacteristic
257C2×Dic5D3×D411yescharacteristic
258D20—32no—
259D20—61no—
260C4×D5—32no—
261C4×D5—32no—
262C4×D5—61no—
263C4×D5—61no—
264C4×D5—121no—
265C4×D5—122no—
266C4×D5—122no—
267C4×D5—121no—
268C4×D5—121no—
269#170—41no—
270#170—41no—
271#170—121no—
272#170—121no—
273C22×D4—151no—
274C23×C4—301no—
275C4×D4—31no—
276C4×D4—51no—
277C4×D4—151no—
278C4×D4—151no—
279C4×D4—301no—
280C4×D4—301no—
281C2×C4⋊C4—151no—
282C2×C22⋊C4—301no—
283C2×C42—151no—
284C4⋊C8—51no—
285C4⋊C8—151no—
286C4⋊C8—301no—
287C22⋊C8—301no—
288C22⋊C8—301no—
289C4×C8—51no—
290C4×C8—151no—
291C4×C8—301no—
292C2×C3×C5—42no—
293C2×C3×C5C2×C22⋊C811yescharacteristic
294C2×C3×C5#41811yescharacteristic
295C2×C3×C5#42111yescharacteristic
296D15—22no—
297D15—42no—
298C23×C3—21no—
299C22×D3—51no—
300C22×D3—104no—
301C22×D3—101no—
302C22×D3—202no—
303C22×D3—202no—
304C3×D4—21no—
305C3×D4D5⋊C812yes—
306C2×C3×C4—51no—
307C2×C3×C4—51no—
308C2×C3×C4—101no—
309C2×C3×C4—201no—
310C2×C3×C4—201no—
311C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
312#67—104no—
313C2×Dic3—21no—
314C2×Dic3—42no—
315C2×Dic3—51no—
316C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
317C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
318D12—52no—
319D12—101no—
320C4×D3—52no—
321C4×D3—52no—
322C4×D3—101no—
323C4×D3—101no—
324C4×D3—201no—
325C4×D3—202no—
326C4×D3—201no—
327C4×D3—201no—
328C4×D3—202no—
329C3×C8—201no—
330C3×C8—201no—
331C3⋊C8—201no—
332C3⋊C8—201no—
333C22×C5—22no—
334C22×C5—41no—
335C22×C5—41no—
336C22×C5D3×C22⋊C411yescharacteristic
337C2×D5—32no—
338C2×D5—61no—
339C2×D5—61no—
340C2×D5—62no—
341C2×D5—128no—
342C2×D5—121no—
343C2×D5—121no—
344C4×C5—61no—
345C4×C5—61no—
346C4×C5—121no—
347C4×C5C2×D3×C811yescharacteristic
348C4×C5D3×M1611yescharacteristic
349Dic5—21no—
350Dic5—32no—
351Dic5—41no—
352Dic5#91111yescharacteristic
353Dic5#91411yescharacteristic
354C24—301no—
355C2×D4—154no—
356C2×D4—151no—
357C2×D4—302no—
358C2×D4—301no—
359C2×D4D3×AGL(1,𝔽5)11yescharacteristic
360C22×C4—61no—
361C22×C4—101no—
362C22×C4—151no—
363C22×C4—151no—
364C22×C4—151no—
365C22×C4—301no—
366C22×C4—301no—
367C22×C4—301no—
368C22×C4—602no—
369C22×C4—602no—
370C2×C8—101no—
371C2×C8—101no—
372C2×C8—301no—
373C2×C8—301no—
374C4⋊C4—31no—
375C4⋊C4—51no—
376C4⋊C4—301no—
377C22⋊C4—61no—
378C22⋊C4—101no—
379C22⋊C4—301no—
380C22⋊C4—301no—
381C42—31no—
382C42—51no—
383C42—151no—
384C42—151no—
385C3×C5#147811yescharacteristic, complemented, Hall
386C22×C3—22no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
390C2×D3—52no—
391C2×D3—101no—
392C2×D3—101no—
393C2×D3—102no—
394C2×D3—208no—
395C2×D3—201no—
396C2×D3—201no—
397C3×C4—51no—
398C3×C4—51no—
399C3×C4—101no—
400C3×C4—201no—
401C3×C4C2×D5⋊C811yescharacteristic
402C3×C4D5⋊M1611yescharacteristic
403Dic3—21no—
404Dic3—21no—
405Dic3—41no—
406Dic3—52no—
407C2×C5—42no—
408C2×C5D3×C22⋊C811yescharacteristic
409C2×C5#477011yescharacteristic
410C2×C5#482111yescharacteristic
411D5—62no—
412D5—122no—
413C23—21no—
414C23—151no—
415C23—304no—
416C23—301no—
417C23—602no—
418C23—602no—
419D4—21no—
420D4—152no—
421D4—304no—
422D4—301no—
423D4#673812yes—
424C2×C4—31no—
425C2×C4—31no—
426C2×C4—51no—
427C2×C4—51no—
428C2×C4—61no—
429C2×C4—101no—
430C2×C4—122no—
431C2×C4—151no—
432C2×C4—152no—
433C2×C4—152no—
434C2×C4—201no—
435C2×C4—201no—
436C2×C4—301no—
437C2×C4—301no—
438C2×C4—601no—
439C2×C4—601no—
440C2×C4—601no—
441C2×C4—602no—
442C2×C4—602no—
443C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
444C8—201no—
445C8—201no—
446C8—601no—
447C8—601no—
448C2×C3—42no—
449C2×C3D5⋊(C22⋊C8)11yescharacteristic
450C2×C3#6576711yescharacteristic
451C2×C3#6579511yescharacteristic
452D3—102no—
453D3—202no—
454C5#6816711yescharacteristic, complemented, Sylow
455C22—22no—
456C22—41no—
457C22—41no—
458C22—152no—
459C22—301no—
460C22—301no—
461C22—302no—
462C22—608no—
463C22—601no—
464C22—601no—
465C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
466C4—51no—
467C4—51no—
468C4—61no—
469C4—61no—
470C4—101no—
471C4—121no—
472C4—152no—
473C4—201no—
474C4C2×#673811yescharacteristic
475C4#9193111yescharacteristic
476C3#1060440311yescharacteristic, complemented, Sylow
477C2—42no—
478C2—302no—
479C2—602no—
480C2#1175193811yescharacteristic
481C2#1175194911yescharacteristic
482C2#1175204211yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC3×C4×C5C22×C8
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×D4×D15C4
cosocleC3×C4×Dic5C23
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#1478
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #11751812C2semidirect
3. #11751777C2semidirect
4. D4⋊(C3⋊#170)C2semidirect
5. C3×D4⋊#170C2semidirect
6. #11746491C2semidirect
7. #11746490C2semidirect
20. C4⋊(C3⋊#170)C22semidirect
21. C4×C3⋊#170C22semidirect
22. C3×C4⋊#170C22semidirect
23. C3×C4×#170C22semidirect
33. D4⋊#170D3semidirect
40. D4×D15C8semidirect
89. C4⋊#170C2×D3semidirect
92. C4×#170C2×D3semidirect
385. C3×C5#1478semidirect
454. C5#68167semidirect
476. C3#10604403semidirect

Maximal subgroups

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

subgroupindex
D4×#12002
#117518122
#117517772
D4⋊(C3⋊#170)2
C3×D4⋊#1702
#117464912
#117464902
#106044033
#681675