Finite Group Databasebeta

← #14282055

Subgroups — #14282055

Order 1920.

436 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 92 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#11755184C211yesmaximal, characteristic
2C4×#6740C211yesmaximal, characteristic
3#11751777C211yesmaximal, characteristic
4#11746801C211yesmaximal, characteristic, complemented
5C3×Q8⋊#170C211yesmaximal, characteristic, complemented
6#11746493C211yesmaximal, characteristic, complemented
7#11746492C211yesmaximal, characteristic, complemented
8#10604648—31nomaximal, Hall
9C2×#6740—21no—
10#91835C411yescharacteristic
11C5×#944C411yescharacteristic
12C3×Q8×Dic5C2211yescharacteristic
13#91469C411yescharacteristic
14#91429—21no—
15#91402—21no—
16C4×#1200C2211yescharacteristic
17#91383C411yescharacteristic
18#91346—21no—
19Dic5×Dic6C2211yescharacteristic
20#91323—21no—
21C4⋊(C3⋊#170)C2211yescharacteristic
22C4×C3⋊#170C2211yescharacteristic
23C3×C4⋊#170C2211yescharacteristic
24C3×C4×#170C2211yescharacteristic
25#91171—21no—
26#91169—21no—
27Dic3×#170—21no—
28#68235—51nomaximal, Hall
29#66062—31no—
30#65680—31no—
31C4×#700—31no—
32Q8⋊#170—31no—
33Q8⋊#170—31no—
34Q8⋊#170—31no—
35Q8⋊#170D311yescharacteristic, complemented
36C2×C3×C5×Q8C2×C411yescharacteristic
37C2×C4×D15C2×C411yescharacteristic
38C2×C5×Dic6C2×C411yescharacteristic
39C2×#1204—21no—
40C2×#1200D411yescharacteristic
41C2×#1200D411yescharacteristic
42C2×C3⋊#170—21no—
43C2×C3⋊#170—21no—
44C2×C3×#170—21no—
45C2×C3×#170—21no—
46#6740—24no—
47#6714—21no—
48C4⋊Dic15C2×C411yescharacteristic
49#6712—21no—
50C5×Dic3⋊C4—21no—
51C5×Dic3⋊C4—21no—
52C4×C5×Dic3C2×C411yescharacteristic
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5C2×C411yescharacteristic
55C3×C4×Dic5—21no—
56C3×C4×Dic5C2311yescharacteristic
57Dic3⋊Dic5—21no—
58Dic3⋊Dic5—21no—
59#6668—21no—
60#6667—21no—
61Dic3×Dic5—21no—
62Dic3×Dic5D411yescharacteristic
63Dic3×Dic5D411yescharacteristic
64#5578—51no—
65#4833—51no—
66C4×ΓL(1,𝔽25)—51no—
67C3×Q8⋊C8—51no—
68#4535—51no—
69#4484—51no—
70#4456—51no—
71C2×#700—61no—
72C5×C4⋊Q8—31no—
73#4092—31no—
74#4092—31no—
75Q8×Dic5—31no—
76Q8×Dic5C2×D311yescharacteristic
77#4043—61no—
78#4038—61no—
79#4036—61no—
80#4033—61no—
81C42×D5—31no—
82#4015—31no—
83#4003—61no—
84#4002—61no—
85C4⋊#170—31no—
86C4⋊#170C2×D311yescharacteristic
87C4×#170—31no—
88C4×#170—61no—
89C4×#170C2×D311yescharacteristic
90#1485—151noSylow
91C22×D15C22⋊C411yescharacteristic
92C3×C5×Q8—21no—
93C3×C5×Q8—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5C22×C411yescharacteristic
96C2×Dic15—21no—
97C2×Dic15C22⋊C411yescharacteristic
98C4×D15—21no—
99C4×D15—21no—
100C2×C5×Dic3—21no—
101C2×C5×Dic3C22⋊C411yescharacteristic
102C2×C5×Dic3C22⋊C411yescharacteristic
103C5×Dic6—21no—
104C5×Dic6—21no—
105C2×C3×Dic5—21no—
106C2×C3×Dic5C2×D411yescharacteristic
107C2×C3×Dic5C2×D411yescharacteristic
108#1204—42no—
109#1200—21no—
110#1200—21no—
111#1200—22no—
112C3⋊#170—22no—
113C3⋊#170—41no—
114C3×#170—22no—
115C3×#170—41no—
116C3×C4×Q8—51no—
117#946—51no—
118#944AGL(1,𝔽5)11yescharacteristic
119C2×ΓL(1,𝔽25)—101no—
120#897—51no—
121#896—101no—
122#889—101no—
123#888—51no—
124#872—101no—
125C42×D3—51no—
126C4×Dic6—51no—
127C4×Dic6—101no—
128C3×C4⋊C8—51no—
129C3×C4×C8—51no—
130(C2×D3)⋊C8—101no—
131#815—101no—
132C8×Dic3—101no—
133C4⋊(C3⋊C8)—51no—
134C4×C3⋊C8—51no—
135C2×C5×Q8—31no—
136C2×C5×Q8C4×D311yescharacteristic
137C2×C4×D5—31no—
138C2×C4×D5—31no—
139C2×C4×D5—31no—
140C2×Dic10—61no—
141C2×#170—21no—
142C2×#170—21no—
143C2×#170—61no—
144C2×#170—61no—
145#700—64no—
146C5×C4⋊C4—61no—
147C5×C4⋊C4—61no—
148C42×C5—31no—
149#685—61no—
150#685—61no—
151C4⋊Dic5—21no—
152C4⋊Dic5—31no—
153C4⋊Dic5—61no—
154C4⋊Dic5—61no—
155C4⋊Dic5C4×D311yescharacteristic
156#683—61no—
157#683—61no—
158C4×Dic5—21no—
159C4×Dic5—31no—
160C4×Dic5—31no—
161C4×Dic5—61no—
162C4×Dic5C22×D311yescharacteristic
163#533—151no—
164#431—151no—
165C4×M16—151no—
166Q8⋊C8—51no—
167Q8⋊C8—151no—
168Q8⋊C8—151no—
169Q8⋊C8—151no—
170C22×C3×C5C2×C22⋊C411yescharacteristic
171C2×D15—21no—
172C2×D15—21no—
173C2×D15—21no—
174C3×C4×C5—41no—
175C3×C4×C5#13111yescharacteristic
176C3×C4×C5#13111yescharacteristic
177Dic15—21no—
178Dic15—41no—
179C3×Dic5—21no—
180C3×Dic5—41no—
181C3×Dic5#13711yescharacteristic
182C3×Dic5#13711yescharacteristic
183C5×Dic3—21no—
184C5×Dic3—41no—
185C5×Dic3#10412yes—
186C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
187C2×C4×D3—51no—
188C2×C4×D3—51no—
189C2×C4×D3—51no—
190C2×Dic6—101no—
191C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
192C2×C3×C8—101no—
193C2×C3×C8—101no—
194C3×C4⋊C4—51no—
195C3×C4⋊C4—101no—
196C3×C42—51no—
197C3×C42—101no—
198(C2×D3)⋊C4—101no—
199(C2×D3)⋊C4—101no—
200C4⋊Dic3—51no—
201C4⋊Dic3—101no—
202Dic3⋊C4—21no—
203Dic3⋊C4—21no—
204Dic3⋊C4—101no—
205Dic3⋊C4—101no—
206Dic3⋊C4—101no—
207C4×Dic3—51no—
208C4×Dic3—51no—
209C4×Dic3—101no—
210C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
211C2×C3⋊C8—101no—
212C2×C3⋊C8—101no—
213ΓL(1,𝔽25)—104no—
214C22×D5—31no—
215C5×Q8—21no—
216C5×Q8—21no—
217C5×Q8—61no—
218C5×Q8—61no—
219C2×C4×C5—21no—
220C2×C4×C5—31no—
221C2×C4×C5—31no—
222C2×C4×C5—61no—
223C2×C4×C5C2×C4×D311yescharacteristic
224C2×Dic5—21no—
225C2×Dic5—31no—
226C2×Dic5—61no—
227C2×Dic5D3×D411yescharacteristic
228C2×Dic5D3×D411yescharacteristic
229C4×D5—62no—
230C4×D5—61no—
231C4×D5—61no—
232C4×D5—61no—
233C4×D5—61no—
234Dic10—122no—
235#170—22no—
236#170—41no—
237#170—62no—
238#170—121no—
239C2×M16—301no—
240C4⋊Q8—31no—
241C4⋊Q8—151no—
242#125—301no—
243C22⋊Q8—151no—
244C22⋊Q8—151no—
245C22⋊Q8—301no—
246C4×Q8—51no—
247C4×Q8—151no—
248C4×Q8—301no—
249#117—301no—
250C2×C42—151no—
251C4⋊C8—51no—
252C4⋊C8—151no—
253C22⋊C8—301no—
254#97—301no—
255C4×C8—51no—
256C4×C8—151no—
257C4×C8—301no—
258C2×C3×C5#40811yescharacteristic
259C2×C3×C5#41911yescharacteristic
260C2×C3×C5C2×#10411yescharacteristic
261D15—41no—
262C22×D3—51no—
263C3×Q8—21no—
264C3×Q8—21no—
265C2×C3×C4—21no—
266C2×C3×C4—51no—
267C2×C3×C4—51no—
268C2×C3×C4—101no—
269C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
270C2×Dic3—21no—
271C2×Dic3—51no—
272C2×Dic3—101no—
273C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
274C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
275C4×D3—101no—
276C4×D3—101no—
277C4×D3—101no—
278C4×D3—101no—
279C4×D3—102no—
280Dic6—21no—
281Dic6—21no—
282Dic6—202no—
283C3×C8—102no—
284C3×C8—201no—
285C3⋊C8—102no—
286C3⋊C8—201no—
287C22×C5D3×C22⋊C411yescharacteristic
288C2×D5—61no—
289C2×D5—61no—
290C2×D5—61no—
291C4×C5—32no—
292C4×C5—41no—
293C4×C5—61no—
294C4×C5—121no—
295C4×C5#90111yescharacteristic
296C4×C5#90711yescharacteristic
297Dic5—21no—
298Dic5—41no—
299Dic5—61no—
300Dic5—121no—
301Dic5#91511yescharacteristic
302Dic5#91811yescharacteristic
303C2×Q8—31no—
304C2×Q8—301no—
305C2×Q8D3×AGL(1,𝔽5)11yescharacteristic
306C22×C4—151no—
307C22×C4—151no—
308C22×C4—151no—
309M16—304no—
310C2×C8—101no—
311C2×C8—101no—
312C2×C8—301no—
313C2×C8—301no—
314C4⋊C4—51no—
315C4⋊C4—61no—
316C4⋊C4—61no—
317C4⋊C4—101no—
318C4⋊C4—151no—
319C4⋊C4—301no—
320C4⋊C4—301no—
321C4⋊C4—301no—
322C4⋊C4—301no—
323C22⋊C4—301no—
324C22⋊C4—301no—
325C42—31no—
326C42—51no—
327C42—101no—
328C42—151no—
329C42—151no—
330C42—301no—
331C3×C5#148511yescharacteristic, complemented, Hall
332C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
333C2×D3—101no—
334C2×D3—101no—
335C2×D3—101no—
336C3×C4—41no—
337C3×C4—51no—
338C3×C4—51no—
339C3×C4—101no—
340C3×C4—201no—
341C3×C4#413111yescharacteristic
342C3×C4#413111yescharacteristic
343Dic3—21no—
344Dic3—41no—
345Dic3—101no—
346Dic3—201no—
347Dic3#401012yes—
348C2×C5#472711yescharacteristic
349C2×C5#480211yescharacteristic
350C2×C5D3×#10411yescharacteristic
351D5—121no—
352C23—151no—
353Q8—21no—
354Q8—21no—
355Q8—61no—
356Q8—61no—
357Q8—602no—
358C2×C4—21no—
359C2×C4—31no—
360C2×C4—31no—
361C2×C4—51no—
362C2×C4—51no—
363C2×C4—61no—
364C2×C4—101no—
365C2×C4—151no—
366C2×C4—302no—
367C2×C4—301no—
368C2×C4—301no—
369C2×C4—301no—
370C2×C4—301no—
371C2×C4—301no—
372C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
373C8—102no—
374C8—201no—
375C8—302no—
376C8—601no—
377C2×C3#6577611yescharacteristic
378C2×C3#6578211yescharacteristic
379C2×C3C2×#401011yescharacteristic
380D3—201no—
381C5#6823511yescharacteristic, complemented, Sylow
382C22—301no—
383C22—301no—
384C22—301no—
385C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
386C4—32no—
387C4—41no—
388C4—51no—
389C4—51no—
390C4—61no—
391C4—101no—
392C4—121no—
393C4—201no—
394C4—301no—
395C4—601no—
396C4#9192711yescharacteristic
397C4#9192911yescharacteristic
398C3#1060464811yescharacteristic, complemented, Sylow
399C2—601no—
400C2#1175196211yescharacteristic
401C2D3×#401011yescharacteristic
402C2#1175204011yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×Q8C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5#1485
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
4. #11746801C2semidirect
5. C3×Q8⋊#170C2semidirect
6. #11746493C2semidirect
7. #11746492C2semidirect
35. Q8⋊#170D3semidirect
331. C3×C5#1485semidirect
381. C5#68235semidirect
398. C3#10604648semidirect

Maximal subgroups

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

subgroupindex
#117551842
C4×#67402
#117517772
#117468012
C3×Q8⋊#1702
#117464932
#117464922
#106046483
#682355