Finite Group Databasebeta

← #14284834

Subgroups — #14284834

Order 1920.

480 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 96 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
1#11753425C211yesmaximal, characteristic
2#11751923C211yesmaximal, characteristic
3#11751760C211yesmaximal, characteristic
4#11746744C211yesmaximal, characteristic, complemented
5C3×#64873C211yesmaximal, characteristic, complemented
6#11746510C211yesmaximal, characteristic, complemented
7#11746509C211yesmaximal, characteristic, complemented
8#10604658—31nomaximal, Hall
9C2×D15⋊Q8—21no—
10C2×#6740—21no—
11C4⋊C4×D15C411yescharacteristic
12C5×#888C411yescharacteristic
13C3×#4034C2211yescharacteristic
14#91469C411yescharacteristic
15#91468C2211yescharacteristic
16#91437C411yescharacteristic
17#91404—21no—
18C4×#1200C2211yescharacteristic
19#91329—21no—
20#91327—21no—
21#91233C2211yescharacteristic
22#91233C2211yescharacteristic
23C3×#4004C2211yescharacteristic
24C3×#4004C2211yescharacteristic
25#91177—21no—
26#91171—21no—
27Dic3×#170—21no—
28#68420—51nomaximal, Hall
29D5×C4⋊Q8—31no—
30#65682—31no—
31#65678—31no—
32#64873—31no—
33#64873—31no—
34#64873—31no—
35#64873D311yescharacteristic, complemented
36C2×C4×D15—21no—
37C2×C4×D15C2×C411yescharacteristic
38C2×C5×Dic6—21no—
39C2×C3×Dic10—21no—
40C2×#1204—21no—
41C2×#1204—21no—
42C2×#1200—21no—
43C2×#1200D411yescharacteristic
44C2×#1200D411yescharacteristic
45D15⋊Q8—42no—
46D15⋊Q8—42no—
47C2×C3⋊#170—21no—
48C2×C3⋊#170—21no—
49C2×C3×#170—21no—
50C2×C3×#170—21no—
51#6740—42no—
52C3×C5×C4⋊C4C2×C411yescharacteristic
53C4⋊Dic15C2×C411yescharacteristic
54#6712—21no—
55C5×C4⋊Dic3C2×C411yescharacteristic
56C5×Dic3⋊C4—21no—
57C4×C5×Dic3C2×C411yescharacteristic
58C3×C4⋊Dic5C2×C411yescharacteristic
59C3×#683—21no—
60C3×C4×Dic5C2311yescharacteristic
61Dic3⋊Dic5—21no—
62#6669—21no—
63#6668—21no—
64Dic3×Dic5D411yescharacteristic
65Dic3×Dic5D411yescharacteristic
66D3×C4⋊Q8—51no—
67#4837—51no—
68#4833—51no—
69C3×#332—51no—
70#4547—51no—
71#4486—51no—
72#4482—51no—
73C2×Q8×D5—61no—
74C2×#700—61no—
75C5×C4⋊Q8—31no—
76#4090—61no—
77D5×C4⋊C4—31no—
78D5×C4⋊C4—31no—
79D5×C4⋊C4—61no—
80#4034—31no—
81#4034—61no—
82#4034C2×D311yescharacteristic
83C42×D5—31no—
84#4015—31no—
85#4004—31no—
86#4004—31no—
87#4004—61no—
88#4004C2×D311yescharacteristic
89#4004C2×D311yescharacteristic
90#4003—61no—
91C4×#170—61no—
92#1546—151noSylow
93C22×D15C22⋊C411yescharacteristic
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5C22×C411yescharacteristic
96C2×Dic15—21no—
97C2×Dic15C22⋊C411yescharacteristic
98C4×D15—22no—
99C4×D15—42no—
100C2×C5×Dic3—21no—
101C2×C5×Dic3C22⋊C411yescharacteristic
102C2×C5×Dic3C22⋊C411yescharacteristic
103C5×Dic6—42no—
104C2×C3×Dic5—21no—
105C2×C3×Dic5C2×D411yescharacteristic
106C2×C3×Dic5C2×D411yescharacteristic
107C3×Dic10—41no—
108C3×Dic10—41no—
109#1204—41no—
110#1204—41no—
111#1204—42no—
112#1200—21no—
113#1200—21no—
114#1200—42no—
115#1200D812yes—
116#1200SD1612yes—
117C3⋊#170—41no—
118C3⋊#170—41no—
119C3×#170—41no—
120C3×#170—41no—
121C2×D3×Q8—101no—
122C3×C4⋊Q8—51no—
123#944—101no—
124C2×ΓL(1,𝔽25)—101no—
125D3×C4⋊C4—51no—
126D3×C4⋊C4—51no—
127D3×C4⋊C4—101no—
128#888—51no—
129#888—101no—
130#888AGL(1,𝔽5)11yescharacteristic
131C42×D3—51no—
132#869—51no—
133C3×C4⋊C8—51no—
134C3×C4⋊C8—51no—
135(C2×D3)⋊C8—101no—
136Dic3⋊C8—101no—
137C8×Dic3—101no—
138C4⋊(C3⋊C8)—51no—
139C4⋊(C3⋊C8)—51no—
140C2×C5×Q8—61no—
141Q8×D5—122no—
142Q8×D5—122no—
143C2×C4×D5—31no—
144C2×C4×D5—31no—
145C2×C4×D5—31no—
146C2×C4×D5—61no—
147C2×C4×D5—61no—
148C2×Dic10—21no—
149C2×Dic10—61no—
150C2×Dic10—61no—
151C2×#170—21no—
152C2×#170—21no—
153C2×#170—61no—
154C2×#170—61no—
155#700—122no—
156C5×C4⋊C4—31no—
157C5×C4⋊C4—61no—
158C5×C4⋊C4C4×D311yescharacteristic
159C42×C5—31no—
160C4⋊Dic5—31no—
161C4⋊Dic5—61no—
162C4⋊Dic5C4×D311yescharacteristic
163#683—21no—
164#683—61no—
165#683—61no—
166#683—61no—
167C4×Dic5—31no—
168C4×Dic5—31no—
169C4×Dic5C22×D311yescharacteristic
170C2×C4⋊Q8—151no—
171#431—151no—
172#423—151no—
173#332—51no—
174#332—151no—
175#332—151no—
176#332—151no—
177C22×C3×C5C2×C22⋊C411yescharacteristic
178C2×D15—21no—
179C2×D15—21no—
180C2×D15#10212yes—
181C3×C4×C5—21no—
182C3×C4×C5—41no—
183Dic15—41no—
184Dic15#10112yes—
185C3×Dic5—41no—
186C3×Dic5C2×D811yescharacteristic
187C3×Dic5C2×SD1611yescharacteristic
188C3×Dic5#13711yescharacteristic
189C3×Dic5#13711yescharacteristic
190C5×Dic3—21no—
191C5×Dic3—41no—
192C5×Dic3#10212yes—
193C2×C3×Q8—101no—
194D3×Q8—202no—
195D3×Q8—202no—
196C2×C4×D3—51no—
197C2×C4×D3—51no—
198C2×C4×D3—51no—
199C2×C4×D3—101no—
200C2×C4×D3—101no—
201C2×Dic6—21no—
202C2×Dic6—101no—
203C2×Dic6—101no—
204C2×C3×C8—101no—
205C2×C3×C8—101no—
206C3×C4⋊C4—51no—
207C3×C4⋊C4—101no—
208C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
209C3×C42—51no—
210C4⋊Dic3—51no—
211C4⋊Dic3—101no—
212C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
213Dic3⋊C4—21no—
214Dic3⋊C4—101no—
215Dic3⋊C4—101no—
216Dic3⋊C4—101no—
217C4×Dic3—51no—
218C4×Dic3—51no—
219C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
220C2×C3⋊C8—101no—
221C2×C3⋊C8—101no—
222ΓL(1,𝔽25)—202no—
223C22×D5—31no—
224C5×Q8—122no—
225C2×C4×C5—21no—
226C2×C4×C5—31no—
227C2×C4×C5—31no—
228C2×C4×C5—61no—
229C2×C4×C5C2×C4×D311yescharacteristic
230C2×Dic5—21no—
231C2×Dic5—31no—
232C2×Dic5—61no—
233C2×Dic5D3×D411yescharacteristic
234C2×Dic5D3×D411yescharacteristic
235C4×D5—32no—
236C4×D5—32no—
237C4×D5—62no—
238C4×D5—61no—
239C4×D5—61no—
240C4×D5—122no—
241C4×D5—122no—
242Dic10—41no—
243Dic10—41no—
244Dic10—122no—
245Dic10—121no—
246Dic10—121no—
247#170—41no—
248#170—41no—
249#170—121no—
250#170—121no—
251C22×Q8—301no—
252C2×M16—301no—
253C4⋊Q8—31no—
254C4⋊Q8—51no—
255C4⋊Q8—151no—
256C4⋊Q8—151no—
257C4⋊Q8—301no—
258C4⋊Q8—301no—
259C2×C4⋊C4—151no—
260C2×C4⋊C4—151no—
261C2×C4⋊C4—301no—
262C2×C42—151no—
263C4⋊C8—51no—
264C4⋊C8—51no—
265C4⋊C8—151no—
266C4⋊C8—151no—
267C4⋊C8—301no—
268C22⋊C8—301no—
269C4×C8—301no—
270C2×C3×C5C2×#10111yescharacteristic
271C2×C3×C5C2×#10211yescharacteristic
272C2×C3×C5#41911yescharacteristic
273D15—22no—
274C22×D3—51no—
275C3×Q8—201no—
276C3×Q8—201no—
277C2×C3×C4—21no—
278C2×C3×C4—51no—
279C2×C3×C4—51no—
280C2×C3×C4—101no—
281C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
282C2×Dic3—21no—
283C2×Dic3—51no—
284C2×Dic3—101no—
285C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
286C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
287C4×D3—52no—
288C4×D3—52no—
289C4×D3—101no—
290C4×D3—101no—
291C4×D3—102no—
292C4×D3—202no—
293C4×D3—202no—
294Dic6—42no—
295Dic6—201no—
296Dic6—201no—
297Dic6—202no—
298C3×C8—201no—
299C3×C8—201no—
300C3⋊C8—201no—
301C3⋊C8—201no—
302C22×C5D3×C22⋊C411yescharacteristic
303C2×D5—32no—
304C2×D5—61no—
305C2×D5—61no—
306C4×C5—21no—
307C4×C5—32no—
308C4×C5—41no—
309C4×C5—61no—
310C4×C5—121no—
311Dic5—32no—
312Dic5—41no—
313Dic5—121no—
314Dic5D3×D811yescharacteristic
315Dic5D3×SD1611yescharacteristic
316Dic5#91511yescharacteristic
317Dic5#91811yescharacteristic
318C2×Q8—61no—
319C2×Q8—101no—
320C2×Q8—301no—
321C2×Q8—301no—
322C2×Q8—602no—
323C2×Q8—602no—
324C22×C4—151no—
325C22×C4—151no—
326C22×C4—151no—
327C22×C4—301no—
328C22×C4—301no—
329M16—602no—
330C2×C8—101no—
331C2×C8—101no—
332C2×C8—301no—
333C2×C8—301no—
334C4⋊C4—31no—
335C4⋊C4—51no—
336C4⋊C4—61no—
337C4⋊C4—101no—
338C4⋊C4—151no—
339C4⋊C4—301no—
340C4⋊C4—301no—
341C4⋊C4—301no—
342C4⋊C4—301no—
343C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
344C42—31no—
345C42—51no—
346C42—151no—
347C42—151no—
348C3×C5#154611yescharacteristic, complemented, Hall
349C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
350C2×D3—52no—
351C2×D3—101no—
352C2×D3—101no—
353C3×C4—21no—
354C3×C4—41no—
355C3×C4—51no—
356C3×C4—51no—
357C3×C4—51no—
358C3×C4—51no—
359C3×C4—201no—
360Dic3—21no—
361Dic3—41no—
362Dic3—52no—
363Dic3—201no—
364Dic3#400712yes—
365C2×C5D3×#10111yescharacteristic
366C2×C5D3×#10211yescharacteristic
367C2×C5#480211yescharacteristic
368D5—62no—
369C23—151no—
370Q8—122no—
371Q8—201no—
372Q8—201no—
373Q8—602no—
374Q8—601no—
375Q8—601no—
376C2×C4—21no—
377C2×C4—31no—
378C2×C4—31no—
379C2×C4—51no—
380C2×C4—51no—
381C2×C4—61no—
382C2×C4—101no—
383C2×C4—152no—
384C2×C4—152no—
385C2×C4—151no—
386C2×C4—302no—
387C2×C4—301no—
388C2×C4—301no—
389C2×C4—301no—
390C2×C4—602no—
391C2×C4—602no—
392C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
393C8—201no—
394C8—201no—
395C8—601no—
396C8—601no—
397C2×C3C2×#400711yescharacteristic
398C2×C3#6578211yescharacteristic
399C2×C3D5⋊#10111yescharacteristic
400D3—102no—
401C5#6842011yescharacteristic, complemented, Sylow
402C22—152no—
403C22—301no—
404C22—301no—
405C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
406C4—21no—
407C4—32no—
408C4—41no—
409C4—51no—
410C4—51no—
411C4—51no—
412C4—51no—
413C4—61no—
414C4—121no—
415C4—152no—
416C4—201no—
417C4—601no—
418C3#1060465811yescharacteristic, complemented, Sylow
419C2—302no—
420C2#1175191811yescharacteristic
421C2D3×#400711yescharacteristic
422C2#1175196211yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C5×C4⋊C4C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1546
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11746744C2semidirect
5. C3×#64873C2semidirect
6. #11746510C2semidirect
7. #11746509C2semidirect
35. #64873D3semidirect
348. C3×C5#1546semidirect
401. C5#68420semidirect
418. C3#10604658semidirect

Maximal subgroups

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

subgroupindex
#117534252
#117519232
#117517602
#117467442
C3×#648732
#117465102
#117465092
#106046583
#684205