Finite Group Databasebeta

← #14291234

Subgroups — #14291234

Order 1920.

368 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 75 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#11756431C211yesmaximal, characteristic
2#11751156C211yesmaximal, characteristic
3#11750804C211yesmaximal, characteristic, complemented
4#11750803C211yesmaximal, characteristic, complemented
5C3×C5×#329C211yesmaximal, characteristic
6#11746286C211yesmaximal, characteristic, complemented
7#11746286C211yesmaximal, characteristic, complemented
8#10599152—31nomaximal, Hall
9C3×C5×#124C2211yescharacteristic
10#91833—21no—
11#91824—21no—
12#91768—21no—
13#91768—21no—
14#91767—21no—
15#91767—21no—
16#91759C2211yescharacteristic
17#91759C2211yescharacteristic
18#91758C2211yescharacteristic
19C3×C5×#97C2211yescharacteristic
20C3×C5×#97C2211yescharacteristic
21#91119—21no—
22#91116—21no—
23#91102—21no—
24#91101—21no—
25#91100—21no—
26#91100—21no—
27#91087C2211yescharacteristic
28#68359—51nomaximal, Hall
29#66006—31no—
30#65344—31no—
31#64992—31no—
32#64991—31no—
33C5×#329D311yescharacteristic
34#64685—31no—
35#64685—31no—
36C2×C3×C5×Q8D411yescharacteristic
37C2×C3×C5×D4D411yescharacteristic
38C22×Dic15—21no—
39C2×Dic30—21no—
40C2×Dic30—21no—
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—21no—
43C3×C5×C22⋊C4—21no—
44C3×C5×C22⋊C4—21no—
45C3×C42×C5C2311yescharacteristic
46#6719—21no—
47#6719—21no—
48#6719—21no—
49C4⋊Dic15—21no—
50C4⋊Dic15—21no—
51C4⋊Dic15D411yescharacteristic
52C4⋊Dic15D411yescharacteristic
53C4⋊Dic15D411yescharacteristic
54C4⋊Dic15D411yescharacteristic
55#6712—21no—
56#6712—21no—
57#6712—21no—
58#6712—21no—
59#6712—21no—
60#6712—21no—
61C4×Dic15—21no—
62C2×C3⋊#168—21no—
63#5672—51no—
64#5055—51no—
65#4703—51no—
66#4702—51no—
67C3×#329D511yescharacteristic
68#4465—51no—
69#4465—51no—
70C5×#124C2×D311yescharacteristic
71#4090—61no—
72#4081—61no—
73#4025—61no—
74#4025—61no—
75#4024—61no—
76#4024—61no—
77#4016—31no—
78#4016—31no—
79#4015—31no—
80C5×#97C2×D311yescharacteristic
81C5×#97C2×D311yescharacteristic
82#3967—61no—
83#3964—61no—
84#3950—61no—
85#3949—61no—
86#3948—61no—
87#3948—61no—
88#3935—31no—
89#1664—151noSylow
90C23×C3×C5—21no—
91C3×C5×Q8—41no—
92C3×C5×D4—41no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×Dic15—21no—
98C2×Dic15—21no—
99C2×Dic15—21no—
100C2×Dic15—21no—
101C2×Dic15—41no—
102C2×Dic15—81no—
103Dic30—42no—
104Dic30—81no—
105C3×C5×C8—22no—
106C3×C5×C8—41no—
107C3⋊#168—41no—
108C3×#124C2×D511yescharacteristic
109#944—101no—
110#935—101no—
111#879—101no—
112#879—101no—
113#878—101no—
114#878—101no—
115#870—51no—
116#870—51no—
117#869—51no—
118C3×#97C2×D511yescharacteristic
119C3×#97C2×D511yescharacteristic
120#835—101no—
121#832—101no—
122#818—101no—
123#817—101no—
124#816—101no—
125#816—101no—
126#803—51no—
127C2×C5×Q8D1211yescharacteristic
128C2×C5×D4D1211yescharacteristic
129C22×Dic5—61no—
130C2×Dic10—61no—
131C2×Dic10—61no—
132C2×C5×C8—21no—
133C2×C5×C8—21no—
134C5×C22⋊C4—21no—
135C5×C22⋊C4—21no—
136C42×C5C22×D311yescharacteristic
137C22⋊Dic5—61no—
138C22⋊Dic5—61no—
139C22⋊Dic5—61no—
140C4⋊Dic5—31no—
141C4⋊Dic5—31no—
142C4⋊Dic5—31no—
143C4⋊Dic5—31no—
144C4⋊Dic5—61no—
145C4⋊Dic5—61no—
146#683—61no—
147#683—61no—
148#683—61no—
149#683—61no—
150#683—61no—
151#683—61no—
152C4×Dic5—61no—
153C2×#168—61no—
154#563—151no—
155#501—151no—
156#491—151no—
157#489—151no—
158#330—151no—
159#330—151no—
160#329D1511yescharacteristic
161C22×C3×C5—41no—
162C22×C3×C5—41no—
163C22×C3×C5—41no—
164C22×C3×C5#12011yescharacteristic
165C3×C4×C5—21no—
166C3×C4×C5—21no—
167C3×C4×C5—21no—
168C3×C4×C5—41no—
169Dic15—41no—
170Dic15—41no—
171Dic15—41no—
172Dic15—41no—
173Dic15—81no—
174C2×C3×Q8D2011yescharacteristic
175C2×C3×D4D2011yescharacteristic
176C22×Dic3—101no—
177C2×Dic6—101no—
178C2×Dic6—101no—
179C2×C3×C8—21no—
180C2×C3×C8—21no—
181C3×C22⋊C4—21no—
182C3×C22⋊C4—21no—
183C3×C42C22×D511yescharacteristic
184#217—101no—
185#217—101no—
186#217—101no—
187C4⋊Dic3—51no—
188C4⋊Dic3—51no—
189C4⋊Dic3—51no—
190C4⋊Dic3—51no—
191C4⋊Dic3—101no—
192C4⋊Dic3—101no—
193Dic3⋊C4—101no—
194Dic3⋊C4—101no—
195Dic3⋊C4—101no—
196Dic3⋊C4—101no—
197Dic3⋊C4—101no—
198Dic3⋊C4—101no—
199C4×Dic3—101no—
200C2×C3⋊C8—101no—
201C23×C5—21no—
202C5×Q8—41no—
203C5×D4—41no—
204C2×C4×C5—21no—
205C2×C4×C5C2×D1211yescharacteristic
206C2×C4×C5D3×D411yescharacteristic
207C2×C4×C5D3×D411yescharacteristic
208C2×Dic5—61no—
209C2×Dic5—61no—
210C2×Dic5—61no—
211C2×Dic5—61no—
212C2×Dic5—121no—
213C2×Dic5—241no—
214Dic10—122no—
215Dic10—241no—
216C5×C8—22no—
217C5×C8—41no—
218#168—121no—
219C4⋊Q8—151no—
220C4⋊Q8—301no—
221#126—301no—
222#126—301no—
223#125—151no—
224#125—151no—
225#124C2×D1511yescharacteristic
226#123—301no—
227C22⋊Q8—301no—
228C22⋊Q8—301no—
229#107—301no—
230#106—301no—
231#103—301no—
232#103—301no—
233#103—301no—
234#102—301no—
235#97—151no—
236#97C2×D1511yescharacteristic
237#97C2×D1511yescharacteristic
238C2×C3×C5—81no—
239C2×C3×C5#45411yescharacteristic
240C2×C3×C5#45511yescharacteristic
241C2×C3×C5#45611yescharacteristic
242C23×C3—21no—
243C3×Q8—41no—
244C3×D4—41no—
245C2×C3×C4—21no—
246C2×C3×C4C2×D2011yescharacteristic
247C2×C3×C4D4×D511yescharacteristic
248C2×C3×C4D4×D511yescharacteristic
249C2×Dic3—101no—
250C2×Dic3—101no—
251C2×Dic3—101no—
252C2×Dic3—101no—
253C2×Dic3—201no—
254C2×Dic3—401no—
255Dic6—202no—
256Dic6—401no—
257C3×C8—22no—
258C3×C8—41no—
259C3⋊C8—201no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5—41no—
263C22×C5#88211yescharacteristic
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—41no—
268Dic5—121no—
269Dic5—121no—
270Dic5—121no—
271Dic5—121no—
272Dic5—241no—
273C2×Q8—301no—
274C2×Q8—301no—
275C2×Q8D6011yescharacteristic
276C2×D4D6011yescharacteristic
277C22×C4—301no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—301no—
281C4⋊C4—151no—
282C4⋊C4—151no—
283C4⋊C4—151no—
284C4⋊C4—151no—
285C4⋊C4—301no—
286C4⋊C4—301no—
287C4⋊C4—301no—
288C4⋊C4—301no—
289C4⋊C4—301no—
290C4⋊C4—301no—
291C4⋊C4—301no—
292C4⋊C4—301no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—301no—
296C22⋊C4—301no—
297C22⋊C4—301no—
298C42—301no—
299C42C22×D1511yescharacteristic
300C3×C5#166411yescharacteristic, complemented, Hall
301C22×C3—41no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3#402811yescharacteristic
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—41no—
309Dic3—201no—
310Dic3—201no—
311Dic3—201no—
312Dic3—201no—
313Dic3—401no—
314C2×C5—81no—
315C2×C5#474611yescharacteristic
316C2×C5#482611yescharacteristic
317C2×C5#482711yescharacteristic
318C23—21no—
319Q8—41no—
320Q8—602no—
321Q8—1201no—
322D4—41no—
323C2×C4—21no—
324C2×C4—301no—
325C2×C4—301no—
326C2×C4—301no—
327C2×C4—301no—
328C2×C4—601no—
329C2×C4—1201no—
330C2×C4C2×D6011yescharacteristic
331C2×C4D4×D1511yescharacteristic
332C2×C4D4×D1511yescharacteristic
333C8—22no—
334C8—41no—
335C8—601no—
336C2×C3—81no—
337C2×C3#6503511yescharacteristic
338C2×C3#6511511yescharacteristic
339C2×C3#6511611yescharacteristic
340C5#6835911yescharacteristic, complemented, Sylow
341C22—41no—
342C22—41no—
343C22—41no—
344C22#9177111yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—601no—
350C4—601no—
351C4—601no—
352C4—601no—
353C4—1201no—
354C3#1059915211yescharacteristic, complemented, Sylow
355C2—81no—
356C2#1175084711yescharacteristic
357C2#1175092711yescharacteristic
358C2#1175092811yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#329C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenter#329D15
hypocenterC3×C5#1664
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
3. #11750804C2semidirect
4. #11750803C2semidirect
6. #11746286C2semidirect
7. #11746286C2semidirect
300. C3×C5#1664semidirect
340. C5#68359semidirect
354. C3#10599152semidirect

Maximal subgroups

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

subgroupindex
#117564312
#117511562
#117508042
#117508032
C3×C5×#3292
#117462862
#105991523
#683595