Subgroups — C₅×#10607 #11933327

Order 1280.

374 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#1965	C₂	1	1	yes	maximal, characteristic
2	C₅×#1950	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#1570	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1565	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1545	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×#331	C₂	1	1	yes	maximal, characteristic
7	C₅×#1292	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#127	C₂²	1	1	yes	characteristic
9	C₅×#431	C₂²	1	1	yes	characteristic
10	C₂×C₅×#108	—	2	1	no	—
11	C₅×#423	C₂²	1	1	yes	characteristic
12	C₅×#423	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×#100	—	2	1	no	—
16	C₂×C₅×#100	—	2	1	no	—
17	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	C₅×#341	—	2	1	no	—
19	C₅×#335	—	2	1	no	—
20	C₅×#334	—	2	1	no	—
21	C₅×#334	—	2	2	no	—
22	C₅×#331	—	2	2	no	—
23	C₅×#331	—	2	1	no	—
24	C₅×#331	—	2	1	no	—
25	#10607	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	C₂²×C₅×D₄	—	2	1	no	—
27	C₂²×C₅×D₄	—	2	1	no	—
28	C₂²×C₅×D₄	Q₈	1	2	yes	—
29	C₂×C₅×M₁₆	—	2	1	no	—
30	C₂×C₅×M₁₆	—	2	1	no	—
31	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
32	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
33	C₂²×C₅×C₈	—	2	1	no	—
34	C₂²×C₅×C₈	—	2	1	no	—
35	C₅×#127	—	2	1	no	—
36	C₅×#127	—	2	1	no	—
37	C₅×#127	—	2	1	no	—
38	C₅×#127	—	2	1	no	—
39	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
40	C₅×#108	—	4	2	no	—
41	C₅×C₄⋊C₈	—	2	1	no	—
42	C₅×C₄⋊C₈	—	2	1	no	—
43	C₅×C₄⋊C₈	—	2	1	no	—
44	C₅×C₄⋊C₈	—	2	1	no	—
45	C₅×C₄⋊C₈	—	2	1	no	—
46	C₅×C₄⋊C₈	—	2	1	no	—
47	C₅×C₄⋊C₈	—	2	1	no	—
48	C₅×C₄⋊C₈	D₄	1	2	yes	—
49	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
50	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
51	C₅×#100	—	4	2	no	—
52	C₅×#100	—	4	2	no	—
53	C₅×C₂²⋊C₈	—	2	1	no	—
54	C₅×#97	—	2	1	no	—
55	C₄×C₅×C₈	—	2	1	no	—
56	C₄×C₅×C₈	—	2	1	no	—
57	#1965	C₂×C₅	1	1	yes	characteristic
58	#1950	C₂×C₅	1	1	yes	characteristic, complemented
59	#1570	C₂×C₅	1	1	yes	characteristic, complemented
60	#1565	C₂×C₅	1	1	yes	characteristic, complemented
61	#1545	C₂×C₅	1	1	yes	characteristic
62	C₂×#331	C₂×C₅	1	1	yes	characteristic
63	#1292	C₂×C₅	1	1	yes	characteristic, complemented
64	C₂⁴×C₅	—	2	2	no	—
65	C₂×C₅×D₄	—	2	2	no	—
66	C₂×C₅×D₄	—	2	2	no	—
67	C₂×C₅×D₄	—	4	1	no	—
68	C₂×C₅×D₄	—	4	1	no	—
69	C₂×C₅×D₄	—	4	1	no	—
70	C₂×C₅×D₄	—	4	1	no	—
71	C₂×C₅×D₄	—	4	1	no	—
72	C₂×C₅×D₄	—	4	1	no	—
73	C₂×C₅×D₄	—	4	1	no	—
74	C₂×C₅×D₄	—	4	1	no	—
75	C₂×C₅×D₄	—	8	1	no	—
76	C₂×C₅×D₄	—	8	1	no	—
77	C₂×C₅×D₄	—	8	2	no	—
78	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
80	C₂²×C₄×C₅	#41	1	1	yes	characteristic
81	C₅×M₁₆	—	2	1	no	—
82	C₅×M₁₆	—	2	1	no	—
83	C₅×M₁₆	—	2	1	no	—
84	C₅×M₁₆	—	4	1	no	—
85	C₅×M₁₆	—	4	1	no	—
86	C₅×M₁₆	—	4	1	no	—
87	C₅×M₁₆	—	4	1	no	—
88	C₅×M₁₆	SD₁₆	1	2	yes	—
89	C₂×C₅×C₈	—	2	1	no	—
90	C₂×C₅×C₈	—	2	2	no	—
91	C₂×C₅×C₈	—	2	1	no	—
92	C₂×C₅×C₈	—	2	1	no	—
93	C₂×C₅×C₈	—	2	1	no	—
94	C₂×C₅×C₈	—	4	1	no	—
95	C₂×C₅×C₈	—	4	1	no	—
96	C₂×C₅×C₈	—	4	1	no	—
97	C₂×C₅×C₈	—	4	1	no	—
98	C₂×C₅×C₈	—	4	1	no	—
99	C₂×C₅×C₈	—	8	1	no	—
100	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
101	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₅	#41	1	1	yes	characteristic
103	C₄²×C₅	#41	1	1	yes	characteristic
104	C₂×#127	C₂²×C₅	1	1	yes	characteristic
105	#431	C₂²×C₅	1	1	yes	characteristic
106	C₂×#108	—	2	1	no	—
107	#423	C₂²×C₅	1	1	yes	characteristic
108	#423	C₂²×C₅	1	1	yes	characteristic
109	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
110	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
111	C₂×#100	—	2	1	no	—
112	C₂×#100	—	2	1	no	—
113	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
114	#341	—	2	1	no	—
115	#335	—	2	1	no	—
116	#334	—	2	1	no	—
117	#334	—	2	2	no	—
118	#331	—	2	2	no	—
119	#331	—	2	1	no	—
120	#331	—	2	1	no	—
121	C₂³×C₅	—	4	2	no	—
122	C₂³×C₅	—	4	2	no	—
123	C₂³×C₅	—	4	2	no	—
124	C₂³×C₅	—	8	2	no	—
125	C₂³×C₅	—	8	2	no	—
126	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
127	C₅×D₄	—	8	2	no	—
128	C₅×D₄	—	8	2	no	—
129	C₅×D₄	—	8	2	no	—
130	C₅×D₄	—	8	1	no	—
131	C₅×D₄	—	8	1	no	—
132	C₅×D₄	—	8	1	no	—
133	C₅×D₄	—	8	1	no	—
134	C₅×D₄	—	8	1	no	—
135	C₅×D₄	—	8	1	no	—
136	C₂×C₄×C₅	—	2	1	no	—
137	C₂×C₄×C₅	—	2	1	no	—
138	C₂×C₄×C₅	—	4	1	no	—
139	C₂×C₄×C₅	#121	1	1	yes	characteristic
140	C₂×C₄×C₅	#121	1	1	yes	characteristic
141	C₂×C₄×C₅	#121	1	1	yes	characteristic
142	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
143	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
144	C₂×C₄×C₅	#126	1	1	yes	characteristic
145	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
146	C₂×C₄×C₅	#135	1	1	yes	characteristic
147	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
148	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
149	C₅×C₈	—	2	2	no	—
150	C₅×C₈	—	4	2	no	—
151	C₅×C₈	—	4	1	no	—
152	C₅×C₈	—	4	1	no	—
153	C₅×C₈	—	4	1	no	—
154	C₅×C₈	—	8	1	no	—
155	C₅×C₈	—	8	1	no	—
156	C₅×C₈	—	8	1	no	—
157	C₂²×D₄	—	2	1	no	—
158	C₂²×D₄	—	2	1	no	—
159	C₂²×D₄	C₅×Q₈	1	2	yes	—
160	C₂×M₁₆	—	2	1	no	—
161	C₂×M₁₆	—	2	1	no	—
162	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
163	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
164	C₂²×C₈	—	2	1	no	—
165	C₂²×C₈	—	2	1	no	—
166	#127	—	2	1	no	—
167	#127	—	2	1	no	—
168	#127	—	2	1	no	—
169	#127	—	2	1	no	—
170	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
171	#108	—	4	2	no	—
172	C₄⋊C₈	—	2	1	no	—
173	C₄⋊C₈	—	2	1	no	—
174	C₄⋊C₈	—	2	1	no	—
175	C₄⋊C₈	—	2	1	no	—
176	C₄⋊C₈	—	2	1	no	—
177	C₄⋊C₈	—	2	1	no	—
178	C₄⋊C₈	—	2	1	no	—
179	C₄⋊C₈	C₅×D₄	1	2	yes	—
180	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
181	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
182	#100	—	4	2	no	—
183	#100	—	4	2	no	—
184	C₂²⋊C₈	—	2	1	no	—
185	#97	—	2	1	no	—
186	C₄×C₈	—	2	1	no	—
187	C₄×C₈	—	2	1	no	—
188	C₂²×C₅	—	2	1	no	—
189	C₂²×C₅	—	2	1	no	—
190	C₂²×C₅	—	8	2	no	—
191	C₂²×C₅	—	8	2	no	—
192	C₂²×C₅	—	8	2	no	—
193	C₂²×C₅	—	16	2	no	—
194	C₂²×C₅	—	16	2	no	—
195	C₂²×C₅	#396	1	1	yes	characteristic
196	C₂²×C₅	#476	1	1	yes	characteristic
197	C₂²×C₅	#478	1	1	yes	characteristic
198	C₄×C₅	—	2	1	no	—
199	C₄×C₅	—	2	1	no	—
200	C₄×C₅	—	2	1	no	—
201	C₄×C₅	#460	1	1	yes	characteristic
202	C₄×C₅	#463	1	1	yes	characteristic
203	C₄×C₅	#465	1	1	yes	characteristic
204	C₄×C₅	#469	1	1	yes	characteristic
205	C₄×C₅	#471	1	1	yes	characteristic
206	C₄×C₅	#472	1	1	yes	characteristic
207	C₂⁴	—	2	2	no	—
208	C₂×D₄	—	2	2	no	—
209	C₂×D₄	—	2	2	no	—
210	C₂×D₄	—	4	1	no	—
211	C₂×D₄	—	4	1	no	—
212	C₂×D₄	—	4	1	no	—
213	C₂×D₄	—	4	1	no	—
214	C₂×D₄	—	4	1	no	—
215	C₂×D₄	—	4	1	no	—
216	C₂×D₄	—	4	1	no	—
217	C₂×D₄	—	4	1	no	—
218	C₂×D₄	—	8	1	no	—
219	C₂×D₄	—	8	1	no	—
220	C₂×D₄	—	8	2	no	—
221	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
222	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
223	C₂²×C₄	C₅×#41	1	1	yes	characteristic
224	M₁₆	—	2	1	no	—
225	M₁₆	—	2	1	no	—
226	M₁₆	—	2	1	no	—
227	M₁₆	—	4	1	no	—
228	M₁₆	—	4	1	no	—
229	M₁₆	—	4	1	no	—
230	M₁₆	—	4	1	no	—
231	M₁₆	C₅×SD₁₆	1	2	yes	—
232	C₂×C₈	—	2	1	no	—
233	C₂×C₈	—	2	1	no	—
234	C₂×C₈	—	2	1	no	—
235	C₂×C₈	—	2	1	no	—
236	C₂×C₈	—	2	2	no	—
237	C₂×C₈	—	4	1	no	—
238	C₂×C₈	—	4	1	no	—
239	C₂×C₈	—	4	1	no	—
240	C₂×C₈	—	4	1	no	—
241	C₂×C₈	—	4	1	no	—
242	C₂×C₈	—	8	1	no	—
243	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
244	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
245	C₄²	C₅×#41	1	1	yes	characteristic
246	C₄²	C₅×#41	1	1	yes	characteristic
247	C₂×C₅	—	2	1	no	—
248	C₂×C₅	—	2	1	no	—
249	C₂×C₅	—	16	2	no	—
250	C₂×C₅	#2063	1	1	yes	characteristic
251	C₂×C₅	#2065	1	1	yes	characteristic
252	C₂×C₅	#2069	1	1	yes	characteristic
253	C₂³	—	4	2	no	—
254	C₂³	—	4	2	no	—
255	C₂³	—	4	2	no	—
256	C₂³	—	8	2	no	—
257	C₂³	—	8	2	no	—
258	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
259	D₄	—	8	2	no	—
260	D₄	—	8	2	no	—
261	D₄	—	8	2	no	—
262	D₄	—	8	1	no	—
263	D₄	—	8	1	no	—
264	D₄	—	8	1	no	—
265	D₄	—	8	1	no	—
266	D₄	—	8	1	no	—
267	D₄	—	8	1	no	—
268	C₂×C₄	—	2	1	no	—
269	C₂×C₄	—	2	1	no	—
270	C₂×C₄	—	4	1	no	—
271	C₂×C₄	C₅×#121	1	1	yes	characteristic
272	C₂×C₄	C₅×#121	1	1	yes	characteristic
273	C₂×C₄	C₅×#121	1	1	yes	characteristic
274	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
275	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
276	C₂×C₄	C₅×#126	1	1	yes	characteristic
277	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
278	C₂×C₄	C₅×#135	1	1	yes	characteristic
279	C₂×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
280	C₂×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
281	C₈	—	2	2	no	—
282	C₈	—	4	2	no	—
283	C₈	—	4	1	no	—
284	C₈	—	4	1	no	—
285	C₈	—	4	1	no	—
286	C₈	—	8	1	no	—
287	C₈	—	8	1	no	—
288	C₈	—	8	1	no	—
289	C₅	#10607	1	1	yes	characteristic, direct product factor, Sylow
290	C₂²	—	2	1	no	—
291	C₂²	—	2	1	no	—
292	C₂²	—	8	2	no	—
293	C₂²	—	8	2	no	—
294	C₂²	—	8	2	no	—
295	C₂²	—	16	2	no	—
296	C₂²	—	16	2	no	—
297	C₂²	C₅×#396	1	1	yes	characteristic
298	C₂²	C₅×#476	1	1	yes	characteristic
299	C₂²	C₅×#478	1	1	yes	characteristic
300	C₄	—	2	1	no	—
301	C₄	—	2	1	no	—
302	C₄	—	2	1	no	—
303	C₄	C₅×#460	1	1	yes	characteristic
304	C₄	C₅×#463	1	1	yes	characteristic
305	C₄	C₅×#465	1	1	yes	characteristic
306	C₄	C₅×#469	1	1	yes	characteristic
307	C₄	C₅×#471	1	1	yes	characteristic
308	C₄	C₅×#472	1	1	yes	characteristic
309	C₂	—	2	1	no	—
310	C₂	—	2	1	no	—
311	C₂	—	16	2	no	—
312	C₂	C₅×#2063	1	1	yes	characteristic
313	C₂	C₅×#2065	1	1	yes	characteristic
314	C₂	C₅×#2069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	#396
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂×C₅×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#1950	C₂	semidirect
3. C₅×#1570	C₂	semidirect
4. C₅×#1565	C₂	semidirect
7. C₅×#1292	C₂	semidirect
25. #10607	C₅	direct (N × H)
58. #1950	C₂×C₅	semidirect
59. #1570	C₂×C₅	semidirect
60. #1565	C₂×C₅	semidirect
63. #1292	C₂×C₅	semidirect
289. C₅	#10607	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#1965	2
C₅×#1950	2
C₅×#1570	2
C₅×#1565	2
C₅×#1545	2
C₂×C₅×#331	2
C₅×#1292	2
#10607	5

Subgroups — C5×#10607 #11933327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10607 #11933327