Finite Group Databasebeta

← #14289407

Subgroups — #14289407

Order 1920.

436 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 86 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#11752636C211yesmaximal, characteristic
2C3×#64982C211yesmaximal, characteristic
3#11746959C211yesmaximal, characteristic, complemented
4#11746917C211yesmaximal, characteristic, complemented
5#11746277C211yesmaximal, characteristic, complemented
6C5×#4456C211yesmaximal, characteristic, complemented
7#11745852C211yesmaximal, characteristic
8#10599053—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C4×C5×Dic6C2211yescharacteristic
11C2×C3×#677—22no—
12C3×#4020C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14#91434—21no—
15Dic3×D20—21no—
16#91407—22no—
17#91368—21no—
18#91364—21no—
19C3×C4×C5×C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22#90990—21no—
23#90989—21no—
24#90974—21no—
25#90972—21no—
26#71270—51nomaximal, Hall
27#65919—31no—
28#65310—31no—
29#65139—31no—
30#64982D311yescharacteristic
31C5×Q8⋊C8—31no—
32#64705—31no—
33#64676—31no—
34C2×Dic30D411yescharacteristic
35C2×C5×Dic6D411yescharacteristic
36C2×C3×D20—21no—
37C2×C3×D20—21no—
38C2×C3×D20D412yes—
39C2×C3×Dic10—21no—
40C2×D5×Dic3—22no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43C4⋊Dic15D411yescharacteristic
44#6712—21no—
45C4×Dic15—21no—
46C2×C3⋊#168—21no—
47C5×C4⋊Dic3D411yescharacteristic
48C5×Dic3⋊C4—21no—
49C4×C5×Dic3—21no—
50C2×C5×C3⋊C8—21no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5—21no—
53C3×#677—44no—
54#6665—22no—
55#6665—22no—
56#6665—22no—
57#5713—51no—
58C3×#492—51no—
59#5091—51no—
60#5091—51no—
61#4544—51no—
62#4456—51no—
63#4456D511yescharacteristic, complemented
64C4×C5×Q8—31no—
65#4093—61no—
66C2×#677—22no—
67#4040—62no—
68#4039—61no—
69#4021—61no—
70#4020C2×D311yescharacteristic
71C4×D20—61no—
72#4015C2×D311yescharacteristic
73C4×Dic10—31no—
74C5×C4⋊C8—31no—
75C4×C5×C8C2×D311yescharacteristic
76#3967—61no—
77#3950—61no—
78#3948—61no—
79#3939—61no—
80C4⋊#168—31no—
81#1630—151noSylow
82C22×C3×D5—22no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—21no—
87C2×Dic15—21no—
88Dic30—21no—
89Dic30—21no—
90C2×C5×Dic3—21no—
91C2×C5×Dic3—21no—
92C5×Dic6—21no—
93C5×Dic6—21no—
94C2×C3×Dic5—41no—
95C3×D20—42no—
96C3×D20—41no—
97C3×D20—41no—
98C3×D20—41no—
99C3×D20—41no—
100C3×Dic10—42no—
101D5×Dic3—82no—
102C3×C5×C8—22no—
103C3⋊#168—41no—
104C5×C3⋊C8—41no—
105C2×C3×SD16—102no—
106C3×C4⋊Q8—51no—
107C3×#127—51no—
108#936—101no—
109#936—101no—
110#935—102no—
111D4×Dic3—101no—
112D4×Dic3—101no—
113C4×Dic6—51no—
114C4×Dic6C2×D511yescharacteristic
115C3×C4×C8C2×D511yescharacteristic
116#810—101no—
117#810—101no—
118#807—101no—
119#807—101no—
120C4⋊(C3⋊C8)—51no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C2×C5×Q8—31no—
123C2×D20—21no—
124C2×D20—21no—
125C2×D20#6712yes—
126C2×C4×D5—62no—
127C2×Dic10—21no—
128C2×Dic10—31no—
129C2×C5×C8—21no—
130C2×C5×C8—61no—
131C5×C4⋊C4—31no—
132C5×C4⋊C4—61no—
133C42×C5—61no—
134C42×C5C22×D311yescharacteristic
135#685—62no—
136#685—62no—
137#685—62no—
138C4⋊Dic5—21no—
139C4⋊Dic5—21no—
140C4⋊Dic5—31no—
141#683—61no—
142C4×Dic5—61no—
143C2×#168—61no—
144#677—44no—
145#559—151no—
146#492—51no—
147#477—151no—
148#477—151no—
149#331—151no—
150Q8⋊C8—31no—
151Q8⋊C8—151no—
152C22×C3×C5#12011yescharacteristic
153C2×C3×D5—42no—
154C2×C3×D5—42no—
155C2×C3×D5—42no—
156C3×C4×C5—21no—
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13711yescharacteristic
160C3×C4×C5#13711yescharacteristic
161Dic15—41no—
162Dic15—41no—
163C3×Dic5—81no—
164C5×Dic3—41no—
165C5×Dic3—41no—
166C2×C3×Q8—101no—
167C2×C3×D4—52no—
168C2×C3×D4—101no—
169C2×C3×D4—101no—
170C22×Dic3—102no—
171C2×Dic6—51no—
172C2×Dic6D2011yescharacteristic
173C3×SD16—204no—
174C2×C3×C8—21no—
175C3×C4⋊C4—101no—
176C3×C4⋊C4—101no—
177C3×C42C22×D511yescharacteristic
178#217—102no—
179#217—102no—
180#217—102no—
181C4⋊Dic3—51no—
182C4⋊Dic3D2011yescharacteristic
183Dic3⋊C4—21no—
184Dic3⋊C4—101no—
185C4×Dic3—21no—
186C4×Dic3—101no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—101no—
189C22×D5—22no—
190C5×Q8—61no—
191C5×Q8—61no—
192C2×C4×C5—61no—
193C2×C4×C5—61no—
194C2×C4×C5D3×D411yescharacteristic
195C2×C4×C5D3×D411yescharacteristic
196C2×C4×C5C2×#6711yescharacteristic
197C2×Dic5—41no—
198C2×Dic5—61no—
199C2×Dic5—61no—
200D20—42no—
201D20—41no—
202D20—41no—
203D20—41no—
204D20—41no—
205C4×D5—242no—
206Dic10—42no—
207Dic10—61no—
208Dic10—61no—
209C5×C8—22no—
210C5×C8—121no—
211#168—121no—
212C2×SD16—102no—
213C4⋊Q8—51no—
214#127—51no—
215#124—301no—
216#124—301no—
217#123—302no—
218C4×Q8—31no—
219C4×Q8—151no—
220C4×D4—301no—
221C4×D4—301no—
222#107—301no—
223#107—301no—
224C4⋊C8—31no—
225C4⋊C8—151no—
226#103—301no—
227#103—301no—
228C4×C8D3×D511yescharacteristic
229C2×C3×C5#45211yescharacteristic
230C2×C3×C5#45211yescharacteristic
231C2×C3×C5#45311yescharacteristic
232C3×D5—82no—
233C23×C3—102no—
234C3×Q8—202no—
235C3×D4—202no—
236C3×D4—201no—
237C3×D4—201no—
238C3×D4—201no—
239C3×D4—201no—
240C2×C3×C4—201no—
241C2×C3×C4C2×D2011yescharacteristic
242C2×C3×C4D4×D511yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C2×Dic3—21no—
245C2×Dic3—21no—
246C2×Dic3—101no—
247C2×Dic3—101no—
248C2×Dic3—402no—
249Dic6—21no—
250Dic6—21no—
251Dic6—101no—
252Dic6—101no—
253C3×C8—22no—
254C3⋊C8—41no—
255C3⋊C8—201no—
256C22×C5#93711yescharacteristic
257C2×D5—42no—
258C2×D5—42no—
259C2×D5—42no—
260C4×C5—21no—
261C4×C5—121no—
262C4×C5—121no—
263C4×C5#91511yescharacteristic
264C4×C5#91511yescharacteristic
265C4×C5#91611yescharacteristic
266C4×C5#91611yescharacteristic
267Dic5—81no—
268Dic5—121no—
269Dic5—121no—
270C2×Q8—31no—
271C2×Q8—101no—
272C2×Q8—151no—
273C2×D4—52no—
274C2×D4—101no—
275C2×D4—101no—
276C22×C4—302no—
277SD16—204no—
278C2×C8—21no—
279C2×C8—61no—
280C2×C8—301no—
281C4⋊C4—31no—
282C4⋊C4—61no—
283C4⋊C4—101no—
284C4⋊C4—101no—
285C4⋊C4—151no—
286C4⋊C4—301no—
287C22⋊C4—302no—
288C22⋊C4—302no—
289C22⋊C4—302no—
290C42—61no—
291C42—301no—
292C42C2×D3×D511yescharacteristic
293C3×C5#163011yescharacteristic, complemented, Hall
294C22×C3—202no—
295C22×C3—202no—
296C22×C3—202no—
297C22×C3#402811yescharacteristic
298C3×C4—21no—
299C3×C4—401no—
300C3×C4#405011yescharacteristic
301C3×C4#405511yescharacteristic
302C3×C4#406211yescharacteristic
303C3×C4#406411yescharacteristic
304Dic3—41no—
305Dic3—41no—
306Dic3—201no—
307Dic3—201no—
308C2×C5#507711yescharacteristic
309C2×C5#517311yescharacteristic
310C2×C5#517311yescharacteristic
311D5—82no—
312C23—102no—
313Q8—61no—
314Q8—61no—
315Q8—202no—
316Q8—301no—
317Q8—301no—
318D4—202no—
319D4—201no—
320D4—201no—
321D4—201no—
322D4—201no—
323C2×C4—61no—
324C2×C4—61no—
325C2×C4—201no—
326C2×C4—301no—
327C2×C4—301no—
328C2×C4—1202no—
329C2×C4D3×D2011yescharacteristic
330C2×C4#677711yescharacteristic
331C2×C4D5×#6711yescharacteristic
332C8—22no—
333C8—121no—
334C8—601no—
335C2×C3—402no—
336C2×C3#6502211yescharacteristic
337C2×C3#6509911yescharacteristic
338C2×C3#6511111yescharacteristic
339C5#7127011yescharacteristic, complemented, Sylow
340C22—202no—
341C22—202no—
342C22—202no—
343C22#9147411yescharacteristic
344C4—21no—
345C4—121no—
346C4—121no—
347C4—401no—
348C4—601no—
349C4—601no—
350C4#9127211yescharacteristic
351C4#9127411yescharacteristic
352C4#9127611yescharacteristic
353C4#9127811yescharacteristic
354C3#1059905311yescharacteristic, complemented, Sylow
355C2—402no—
356C2#1174711411yescharacteristic
357C2#1174814711yescharacteristic
358C2#1174814811yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radicalC3×#4020C22
hypercenterC4×C8D3×D5
hypocenterC3×C5#1630
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
3. #11746959C2semidirect
4. #11746917C2semidirect
5. #11746277C2semidirect
6. C5×#4456C2semidirect
63. #4456D5semidirect
293. C3×C5#1630semidirect
339. C5#71270semidirect
354. C3#10599053semidirect

Maximal subgroups

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

subgroupindex
#117526362
C3×#649822
#117469592
#117469172
#117462772
C5×#44562
#117458522
#105990533
#712705