Finite Group Databasebeta

← #14291039

Subgroups — #14291039

Order 1920.

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

normal subgroups only

This group has 392 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#11756458C211yesmaximal, characteristic
2C3×C5×#501C211yesmaximal, characteristic, complemented
3#11751187C211yesmaximal, characteristic
4#11751182C211yesmaximal, characteristic, complemented
5#11746364C211yesmaximal, characteristic, complemented
6#11746286C211yesmaximal, characteristic, complemented
7#11746285C211yesmaximal, characteristic
8#10602184—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#125C2211yescharacteristic
11C2×#6718—21no—
12C2×#6717—21no—
13#91787—21no—
14#91787—21no—
15#91786—21no—
16#91785—21no—
17#91783—21no—
18#91777—21no—
19#91764C2211yescharacteristic
20#91759C2211yescharacteristic
21C3×C5×#107—21no—
22C3×C5×#106—21no—
23C3×C5×#97C2211yescharacteristic
24#91092—21no—
25#91091—21no—
26#91087C2211yescharacteristic
27#91087C2211yescharacteristic
28#71391—51nomaximal, Hall
29#66033—31no—
30C5×#501D311yescharacteristic, complemented
31#65375—31no—
32#65369—31no—
33#64763—31no—
34#64685—31no—
35#64684—31no—
36C2×C3×C5×Q8—21no—
37C2×D60D411yescharacteristic
38C2×C4×D15—21no—
39C2×Dic30—21no—
40C2×Dic30D411yescharacteristic
41C2×C3×C5×C8—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C42×C5C2311yescharacteristic
49#6718—42no—
50#6717—42no—
51#6714—21no—
52#6714—21no—
53#6714—21no—
54#6714—21no—
55#6714—21no—
56C4⋊Dic15—21no—
57C4⋊Dic15D411yescharacteristic
58C4⋊Dic15D411yescharacteristic
59#6712—21no—
60#6712—21no—
61#6712—21no—
62C4×Dic15—21no—
63C2×C3⋊#168—21no—
64C2×C3⋊#168—21no—
65#5699—51no—
66C3×#501D511yescharacteristic, complemented
67#5086—51no—
68#5081—51no—
69#4543—51no—
70#4465—51no—
71#4464—51no—
72C5×C4⋊Q8C2×D311yescharacteristic
73C5×#125C2×D311yescharacteristic
74C2×#689—61no—
75C2×#688—61no—
76#4044—61no—
77#4044—61no—
78#4043—61no—
79#4042—61no—
80#4040—61no—
81#4034—61no—
82#4021—31no—
83#4016—31no—
84C5×#107—21no—
85C5×#106—21no—
86C5×#97C2×D311yescharacteristic
87#3940—61no—
88#3939—61no—
89#3935—31no—
90#3935—31no—
91#1660—151noSylow
92C22×D15—21no—
93C3×C5×Q8—41no—
94C3×C5×Q8—41no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×Dic15—21no—
102C2×Dic15—21no—
103C2×Dic15—21no—
104D60—41no—
105C4×D15—81no—
106Dic30—41no—
107Dic30—81no—
108C3×C5×C8—22no—
109C3⋊#168—22no—
110C3⋊#168—22no—
111C3×C4⋊Q8C2×D511yescharacteristic
112C3×#125C2×D511yescharacteristic
113C2×#216—101no—
114C2×#215—101no—
115#898—101no—
116#898—101no—
117#897—101no—
118#896—101no—
119#894—101no—
120#888—101no—
121#875—51no—
122#870—51no—
123C3×#107—21no—
124C3×#106—21no—
125C3×#97C2×D511yescharacteristic
126#808—101no—
127#807—101no—
128#803—51no—
129#803—51no—
130C2×C5×Q8—21no—
131C2×D20—31no—
132C2×C4×D5—61no—
133C2×Dic10—31no—
134C2×Dic10—61no—
135C2×C5×C8—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—21no—
139C5×C4⋊C4—21no—
140C5×C4⋊C4#6711yescharacteristic
141C5×C4⋊C4#6711yescharacteristic
142C42×C5C22×D311yescharacteristic
143#689—122no—
144#688—122no—
145#685—61no—
146#685—61no—
147#685—61no—
148#685—61no—
149#685—61no—
150C4⋊Dic5—31no—
151C4⋊Dic5—31no—
152C4⋊Dic5—61no—
153#683—61no—
154#683—61no—
155#683—61no—
156C4×Dic5—61no—
157C2×#168—61no—
158C2×#168—61no—
159#563—151no—
160#501—151no—
161#501D1511yescharacteristic, complemented
162#497—151no—
163#330—151no—
164#330—151no—
165#329—151no—
166C22×C3×C5#12011yescharacteristic
167C2×D15—41no—
168C2×D15—41no—
169C2×D15—41no—
170C3×C4×C5—21no—
171C3×C4×C5—21no—
172C3×C4×C5—21no—
173C3×C4×C5—41no—
174C3×C4×C5—41no—
175C3×C4×C5—81no—
176Dic15—41no—
177Dic15—41no—
178Dic15—41no—
179C2×C3×Q8—21no—
180C2×D12—51no—
181C2×C4×D3—101no—
182C2×Dic6—51no—
183C2×Dic6—101no—
184C2×C3×C8—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4C22⋊D511yescharacteristic
190C3×C4⋊C4C22⋊D511yescharacteristic
191C3×C42C22×D511yescharacteristic
192#216—202no—
193#215—202no—
194(C2×D3)⋊C4—101no—
195(C2×D3)⋊C4—101no—
196(C2×D3)⋊C4—101no—
197(C2×D3)⋊C4—101no—
198(C2×D3)⋊C4—101no—
199C4⋊Dic3—51no—
200C4⋊Dic3—51no—
201C4⋊Dic3—101no—
202Dic3⋊C4—101no—
203Dic3⋊C4—101no—
204Dic3⋊C4—101no—
205C4×Dic3—101no—
206C2×C3⋊C8—101no—
207C2×C3⋊C8—101no—
208C22×D5—61no—
209C5×Q8—41no—
210C5×Q8—41no—
211C2×C4×C5—21no—
212C2×C4×C5—21no—
213C2×C4×C5—41no—
214C2×C4×C5D3×D411yescharacteristic
215C2×C4×C5D3×D411yescharacteristic
216C2×C4×C5C2×#6711yescharacteristic
217C2×Dic5—61no—
218C2×Dic5—61no—
219C2×Dic5—61no—
220D20—121no—
221C4×D5—241no—
222Dic10—121no—
223Dic10—241no—
224C5×C8—22no—
225#168—62no—
226#168—62no—
227C2×Q16—301no—
228C2×SD16—301no—
229C4⋊Q8—301no—
230C4⋊Q8C2×D1511yescharacteristic
231#126—301no—
232#126—301no—
233#125—151no—
234#125C2×D1511yescharacteristic
235#124—151no—
236#123—301no—
237C22⋊Q8—301no—
238C22⋊Q8—301no—
239#107—21no—
240#107—301no—
241#106—21no—
242#106—301no—
243#97—151no—
244#97—151no—
245#97C2×D1511yescharacteristic
246C2×C3×C5#45311yescharacteristic
247C2×C3×C5#45611yescharacteristic
248C2×C3×C5#45611yescharacteristic
249D15—81no—
250C22×D3—101no—
251C3×Q8—41no—
252C3×Q8—41no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—41no—
256C2×C3×C4D4×D511yescharacteristic
257C2×C3×C4D4×D511yescharacteristic
258C2×C3×C4C2×C22⋊D511yescharacteristic
259C2×Dic3—101no—
260C2×Dic3—101no—
261C2×Dic3—101no—
262D12—201no—
263C4×D3—401no—
264Dic6—201no—
265Dic6—401no—
266C3×C8—22no—
267C3⋊C8—102no—
268C3⋊C8—102no—
269C22×C5#93711yescharacteristic
270C2×D5—121no—
271C2×D5—121no—
272C2×D5—121no—
273C4×C5—21no—
274C4×C5—21no—
275C4×C5—21no—
276C4×C5—41no—
277C4×C5—41no—
278C4×C5—81no—
279Dic5—121no—
280Dic5—121no—
281Dic5—121no—
282C2×Q8—21no—
283C2×Q8—151no—
284C2×Q8—301no—
285C2×D4—151no—
286C22×C4—301no—
287Q16—602no—
288SD16—602no—
289C2×C8—21no—
290C2×C8—301no—
291C2×C8—301no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—151no—
297C4⋊C4—151no—
298C4⋊C4—301no—
299C4⋊C4—301no—
300C4⋊C4—301no—
301C4⋊C4—301no—
302C4⋊C4#122011yescharacteristic
303C4⋊C4#122011yescharacteristic
304C22⋊C4—301no—
305C22⋊C4—301no—
306C22⋊C4—301no—
307C22⋊C4—301no—
308C22⋊C4—301no—
309C42—301no—
310C42C22×D1511yescharacteristic
311C3×C5#166011yescharacteristic, complemented, Hall
312C22×C3#408311yescharacteristic
313C2×D3—201no—
314C2×D3—201no—
315C2×D3—201no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—41no—
320C3×C4—41no—
321C3×C4—81no—
322Dic3—201no—
323Dic3—201no—
324Dic3—201no—
325C2×C5#509511yescharacteristic
326C2×C5#519811yescharacteristic
327C2×C5#520511yescharacteristic
328D5—241no—
329C23—301no—
330Q8—41no—
331Q8—41no—
332Q8—601no—
333Q8—1201no—
334D4—601no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—301no—
339C2×C4—301no—
340C2×C4—301no—
341C2×C4—1201no—
342C2×C4D4×D1511yescharacteristic
343C2×C4D4×D1511yescharacteristic
344C2×C4C2×#122011yescharacteristic
345C8—22no—
346C8—302no—
347C8—302no—
348C2×C3#6538411yescharacteristic
349C2×C3#6548711yescharacteristic
350C2×C3#6549411yescharacteristic
351D3—401no—
352C5#7139111yescharacteristic, complemented, Sylow
353C22—601no—
354C22—601no—
355C22—601no—
356C22#9182611yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—81no—
363C4—601no—
364C4—601no—
365C4—601no—
366C3#1060218411yescharacteristic, complemented, Sylow
367C2—1201no—
368C2#1175119611yescharacteristic
369C2#1175129911yescharacteristic
370C2#1175130611yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#501C2
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenter#501D15
hypocenterC3×C5#1660
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. C3×C5×#501C2semidirect
4. #11751182C2semidirect
5. #11746364C2semidirect
6. #11746286C2semidirect
30. C5×#501D3semidirect
66. C3×#501D5semidirect
161. #501D15semidirect
311. C3×C5#1660semidirect
352. C5#71391semidirect
366. C3#10602184semidirect

Maximal subgroups

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

subgroupindex
#117564582
C3×C5×#5012
#117511872
#117511822
#117463642
#117462862
#117462852
#106021843
#713915