Subgroups — C₅×#12038 #11934758

Order 1280.

244 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2169	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₄×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₈×D₈	C₂	1	1	yes	maximal, characteristic
4	C₅×#1370	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×D₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×D₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1311	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×M₃₂	—	2	1	no	—
9	C₂²×C₅×C₁₆	—	2	1	no	—
10	C₄×C₅×D₈	C₄	1	1	yes	characteristic
11	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
12	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
13	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
14	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
15	C₅×C₂²⋊C₁₆	—	2	1	no	—
16	C₅×C₂²⋊C₁₆	—	2	1	no	—
17	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
18	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
19	C₅×#335	C₄	1	1	yes	characteristic
20	C₅×D₄⋊C₈	C₄	1	1	yes	characteristic
21	C₅×D₄⋊C₈	C₄	1	1	yes	characteristic
22	C₅×C₈²	C₂²	1	1	yes	characteristic
23	#12038	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂×C₅×D₈	C₈	1	1	yes	characteristic
25	C₂²×C₅×C₈	—	2	1	no	—
26	C₂²×C₅×C₈	—	2	1	no	—
27	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
28	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
29	C₅×M₃₂	—	4	2	no	—
30	C₂×C₅×C₁₆	—	2	1	no	—
31	C₂×C₅×C₁₆	—	2	1	no	—
32	C₂×C₅×C₁₆	—	2	1	no	—
33	C₂×C₅×C₁₆	—	4	2	no	—
34	C₂×C₅×C₁₆	D₄	1	1	yes	characteristic
35	C₂×C₅×C₁₆	D₄	1	1	yes	characteristic
36	C₅×#107	C₈	1	1	yes	characteristic
37	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
38	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
39	C₅×#102	C₈	1	1	yes	characteristic
40	C₅×#102	C₈	1	1	yes	characteristic
41	C₅×C₂²⋊C₈	—	2	1	no	—
42	C₅×C₂²⋊C₈	—	2	1	no	—
43	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
44	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
45	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
46	#2169	C₂×C₅	1	1	yes	characteristic, complemented
47	D₄×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
48	C₈×D₈	C₂×C₅	1	1	yes	characteristic
49	#1370	C₂×C₅	1	1	yes	characteristic, complemented
50	D₄⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
51	D₄⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
52	#1311	C₂×C₅	1	1	yes	characteristic, complemented
53	C₂×C₅×D₄	C₂×C₈	1	1	yes	characteristic
54	C₂×C₅×D₄	C₂×C₈	1	1	yes	characteristic
55	C₂²×C₄×C₅	—	2	1	no	—
56	C₂²×C₄×C₅	—	2	1	no	—
57	C₅×D₈	—	2	2	no	—
58	C₂×C₅×C₈	—	2	1	no	—
59	C₂×C₅×C₈	—	2	1	no	—
60	C₂×C₅×C₈	—	2	1	no	—
61	C₂×C₅×C₈	—	4	1	no	—
62	C₂×C₅×C₈	—	4	1	no	—
63	C₂×C₅×C₈	—	4	1	no	—
64	C₂×C₅×C₈	—	4	1	no	—
65	C₂×C₅×C₈	C₂×C₈	1	1	yes	characteristic
66	C₂×C₅×C₈	C₂×C₈	1	1	yes	characteristic
67	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
68	C₂×C₅×C₈	#41	1	1	yes	characteristic
69	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
70	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
71	C₅×C₂²⋊C₄	—	2	1	no	—
72	C₅×C₂²⋊C₄	—	2	1	no	—
73	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
74	C₅×C₁₆	—	2	2	no	—
75	C₅×C₁₆	—	2	1	no	—
76	C₅×C₁₆	—	4	1	no	—
77	C₅×C₁₆	—	4	1	no	—
78	C₅×C₁₆	D₈	1	2	yes	complemented
79	C₂×M₃₂	—	2	1	no	—
80	C₂²×C₁₆	—	2	1	no	—
81	C₄×D₈	C₄×C₅	1	1	yes	characteristic
82	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
83	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
84	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
85	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
86	C₂²⋊C₁₆	—	2	1	no	—
87	C₂²⋊C₁₆	—	2	1	no	—
88	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic
89	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic
90	#335	C₄×C₅	1	1	yes	characteristic
91	D₄⋊C₈	C₄×C₅	1	1	yes	characteristic
92	D₄⋊C₈	C₄×C₅	1	1	yes	characteristic
93	C₈²	C₂²×C₅	1	1	yes	characteristic
94	C₂³×C₅	—	2	1	no	—
95	C₂³×C₅	—	2	1	no	—
96	C₅×D₄	—	2	1	no	—
97	C₅×D₄	—	2	1	no	—
98	C₅×D₄	—	2	1	no	—
99	C₅×D₄	M₃₂	1	2	yes	complemented
100	C₂×C₄×C₅	—	2	1	no	—
101	C₂×C₄×C₅	—	2	1	no	—
102	C₂×C₄×C₅	—	4	1	no	—
103	C₂×C₄×C₅	—	4	1	no	—
104	C₂×C₄×C₅	—	4	1	no	—
105	C₂×C₄×C₅	—	4	1	no	—
106	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
107	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
108	C₂×C₄×C₅	#131	1	1	yes	characteristic
109	C₅×C₈	—	2	1	no	—
110	C₅×C₈	—	2	1	no	—
111	C₅×C₈	—	2	1	no	—
112	C₅×C₈	—	4	1	no	—
113	C₅×C₈	—	4	1	no	—
114	C₅×C₈	—	4	1	no	—
115	C₅×C₈	C₂×D₈	1	1	yes	characteristic
116	C₅×C₈	#135	1	1	yes	characteristic
117	C₂×D₈	C₅×C₈	1	1	yes	characteristic
118	C₂²×C₈	—	2	1	no	—
119	C₂²×C₈	—	2	1	no	—
120	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
121	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
122	M₃₂	—	4	2	no	—
123	C₂×C₁₆	—	2	1	no	—
124	C₂×C₁₆	—	2	1	no	—
125	C₂×C₁₆	—	2	1	no	—
126	C₂×C₁₆	—	4	2	no	—
127	C₂×C₁₆	C₅×D₄	1	1	yes	characteristic
128	C₂×C₁₆	C₅×D₄	1	1	yes	characteristic
129	#107	C₅×C₈	1	1	yes	characteristic
130	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
131	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
132	#102	C₅×C₈	1	1	yes	characteristic
133	#102	C₅×C₈	1	1	yes	characteristic
134	C₂²⋊C₈	—	2	1	no	—
135	C₂²⋊C₈	—	2	1	no	—
136	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
137	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
138	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
139	C₂²×C₅	—	2	2	no	—
140	C₂²×C₅	—	4	1	no	—
141	C₂²×C₅	—	4	1	no	—
142	C₂²×C₅	—	4	1	no	—
143	C₂²×C₅	—	4	1	no	—
144	C₂²×C₅	—	4	1	no	—
145	C₂²×C₅	C₈×D₄	1	1	yes	characteristic
146	C₄×C₅	—	2	1	no	—
147	C₄×C₅	—	4	1	no	—
148	C₄×C₅	—	4	1	no	—
149	C₄×C₅	C₄×D₈	1	1	yes	characteristic
150	C₄×C₅	#443	1	1	yes	characteristic
151	C₄×C₅	C₂×M₃₂	1	1	yes	characteristic
152	C₄×C₅	#504	1	1	yes	characteristic
153	C₂×D₄	C₂×C₅×C₈	1	1	yes	characteristic
154	C₂×D₄	C₂×C₅×C₈	1	1	yes	characteristic
155	C₂²×C₄	—	2	1	no	—
156	C₂²×C₄	—	2	1	no	—
157	D₈	—	2	2	no	—
158	C₂×C₈	—	2	1	no	—
159	C₂×C₈	—	2	1	no	—
160	C₂×C₈	—	2	1	no	—
161	C₂×C₈	—	4	1	no	—
162	C₂×C₈	—	4	1	no	—
163	C₂×C₈	—	4	1	no	—
164	C₂×C₈	—	4	1	no	—
165	C₂×C₈	C₂×C₅×C₈	1	1	yes	characteristic
166	C₂×C₈	C₂×C₅×C₈	1	1	yes	characteristic
167	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
168	C₂×C₈	C₅×#41	1	1	yes	characteristic
169	C₄⋊C₄	C₂×C₅×C₈	1	1	yes	characteristic
170	C₄⋊C₄	C₂×C₅×C₈	1	1	yes	characteristic
171	C₂²⋊C₄	—	2	1	no	—
172	C₂²⋊C₄	—	2	1	no	—
173	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
174	C₁₆	—	2	2	no	—
175	C₁₆	—	2	1	no	—
176	C₁₆	—	4	1	no	—
177	C₁₆	—	4	1	no	—
178	C₁₆	C₅×D₈	1	2	yes	complemented
179	C₂×C₅	—	4	2	no	—
180	C₂×C₅	—	8	1	no	—
181	C₂×C₅	C₈×D₈	1	1	yes	characteristic
182	C₂×C₅	#2168	1	1	yes	characteristic
183	C₂×C₅	#2171	1	1	yes	characteristic
184	C₂³	—	2	1	no	—
185	C₂³	—	2	1	no	—
186	D₄	—	2	1	no	—
187	D₄	—	2	1	no	—
188	D₄	—	2	1	no	—
189	D₄	C₅×M₃₂	1	2	yes	complemented
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	2	1	no	—
192	C₂×C₄	—	4	1	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	4	1	no	—
195	C₂×C₄	—	4	1	no	—
196	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
197	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
198	C₂×C₄	C₅×#131	1	1	yes	characteristic
199	C₈	—	2	1	no	—
200	C₈	—	2	1	no	—
201	C₈	—	2	1	no	—
202	C₈	—	4	1	no	—
203	C₈	—	4	1	no	—
204	C₈	—	4	1	no	—
205	C₈	C₂×C₅×D₈	1	1	yes	characteristic
206	C₈	C₅×#135	1	1	yes	characteristic
207	C₅	#12038	1	1	yes	characteristic, direct product factor, Sylow
208	C₂²	—	2	2	no	—
209	C₂²	—	4	1	no	—
210	C₂²	—	4	1	no	—
211	C₂²	—	4	1	no	—
212	C₂²	—	4	1	no	—
213	C₂²	—	4	1	no	—
214	C₂²	C₅×C₈×D₄	1	1	yes	characteristic
215	C₄	—	2	1	no	—
216	C₄	—	4	1	no	—
217	C₄	—	4	1	no	—
218	C₄	C₄×C₅×D₈	1	1	yes	characteristic
219	C₄	C₅×#443	1	1	yes	characteristic
220	C₄	C₂×C₅×M₃₂	1	1	yes	characteristic
221	C₄	C₅×#504	1	1	yes	characteristic
222	C₂	—	4	2	no	—
223	C₂	—	8	1	no	—
224	C₂	C₅×C₈×D₈	1	1	yes	characteristic
225	C₂	C₅×#2168	1	1	yes	characteristic
226	C₂	C₅×#2171	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅×C₈	C₂×D₄
commutator	C₂×C₄	C₂²×C₅×C₈
Frattini, cosocle	C₄×C₈	C₂³×C₅
socle	C₂²×C₅	C₈×D₄
prime radical	C₂×C₅×D₈	C₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ C₄×C₅×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2169	C₂	semidirect
2. C₅×D₄×C₁₆	C₂	semidirect
4. C₅×#1370	C₂	semidirect
5. C₅×D₄⋊C₁₆	C₂	semidirect
6. C₅×D₄⋊C₁₆	C₂	semidirect
7. C₅×#1311	C₂	semidirect
23. #12038	C₅	direct (N × H)
46. #2169	C₂×C₅	semidirect
47. D₄×C₁₆	C₂×C₅	semidirect
49. #1370	C₂×C₅	semidirect
50. D₄⋊C₁₆	C₂×C₅	semidirect
51. D₄⋊C₁₆	C₂×C₅	semidirect
52. #1311	C₂×C₅	semidirect
78. C₅×C₁₆	D₈	semidirect
99. C₅×D₄	M₃₂	semidirect
178. C₁₆	C₅×D₈	semidirect
189. D₄	C₅×M₃₂	semidirect
207. C₅	#12038	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×#2169	2
C₅×D₄×C₁₆	2
C₅×C₈×D₈	2
C₅×#1370	2
C₅×D₄⋊C₁₆	2
C₅×#1311	2
#12038	5

Subgroups — C5×#12038 #11934758

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#12038 #11934758