Subgroups — C₅×#12053 #11934773

Order 1280.

206 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2183	C₂	1	1	yes	maximal, characteristic
2	C₅×Q₈×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₅×C₈×Q₁₆	C₂	1	1	yes	maximal, characteristic
4	C₅×#1370	C₂	1	1	yes	maximal, characteristic
5	C₅×Q₈⋊C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₅×Q₈⋊C₁₆	C₂	1	1	yes	maximal, characteristic
7	C₅×#1311	C₂	1	1	yes	maximal, characteristic
8	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
9	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
10	C₄×C₅×Q₁₆	C₄	1	1	yes	characteristic
11	C₅×C₄⋊C₁₆	—	2	1	no	—
12	C₅×C₄⋊C₁₆	—	2	1	no	—
13	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
14	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
15	C₅×#346	—	2	1	no	—
16	C₄×C₅×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×Q₈⋊C₈	C₄	1	1	yes	characteristic
21	C₅×Q₈⋊C₈	C₄	1	1	yes	characteristic
22	C₅×C₈²	C₂²	1	1	yes	characteristic
23	#12053	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂×C₅×Q₁₆	C₈	1	1	yes	characteristic
25	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
26	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
27	C₂×C₅×C₁₆	—	2	1	no	—
28	C₂×C₅×C₁₆	—	2	1	no	—
29	C₂×C₅×C₁₆	—	2	1	no	—
30	C₂×C₅×C₁₆	D₄	1	1	yes	characteristic
31	C₂×C₅×C₁₆	D₄	1	1	yes	characteristic
32	C₅×#107	C₈	1	1	yes	characteristic
33	C₅×C₄⋊C₈	—	2	1	no	—
34	C₅×C₄⋊C₈	—	2	1	no	—
35	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
37	C₅×#103	C₈	1	1	yes	characteristic
38	C₅×#103	C₈	1	1	yes	characteristic
39	C₄×C₅×C₈	—	2	1	no	—
40	C₄×C₅×C₈	—	2	1	no	—
41	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
42	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
43	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
44	#2183	C₂×C₅	1	1	yes	characteristic
45	Q₈×C₁₆	C₂×C₅	1	1	yes	characteristic
46	C₈×Q₁₆	C₂×C₅	1	1	yes	characteristic
47	#1370	C₂×C₅	1	1	yes	characteristic
48	Q₈⋊C₁₆	C₂×C₅	1	1	yes	characteristic
49	Q₈⋊C₁₆	C₂×C₅	1	1	yes	characteristic
50	#1311	C₂×C₅	1	1	yes	characteristic
51	C₂×C₅×Q₈	C₂×C₈	1	1	yes	characteristic
52	C₂×C₅×Q₈	C₂×C₈	1	1	yes	characteristic
53	C₅×Q₁₆	—	2	2	no	—
54	C₂×C₅×C₈	—	2	1	no	—
55	C₂×C₅×C₈	—	2	1	no	—
56	C₂×C₅×C₈	—	2	1	no	—
57	C₂×C₅×C₈	C₂×C₈	1	1	yes	characteristic
58	C₂×C₅×C₈	C₂×C₈	1	1	yes	characteristic
59	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
60	C₂×C₅×C₈	#41	1	1	yes	characteristic
61	C₅×C₄⋊C₄	—	2	1	no	—
62	C₅×C₄⋊C₄	—	2	1	no	—
63	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
64	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
65	C₄²×C₅	—	2	1	no	—
66	C₄²×C₅	—	2	1	no	—
67	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
68	C₅×C₁₆	—	2	2	no	—
69	C₅×C₁₆	—	2	1	no	—
70	C₅×C₁₆	—	4	1	no	—
71	C₅×C₁₆	—	4	1	no	—
72	C₅×C₁₆	Q₁₆	1	2	yes	complemented
73	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
74	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
75	C₄×Q₁₆	C₄×C₅	1	1	yes	characteristic
76	C₄⋊C₁₆	—	2	1	no	—
77	C₄⋊C₁₆	—	2	1	no	—
78	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
79	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
80	#346	—	2	1	no	—
81	C₄×C₁₆	—	2	1	no	—
82	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic
83	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic
84	#335	C₄×C₅	1	1	yes	characteristic
85	Q₈⋊C₈	C₄×C₅	1	1	yes	characteristic
86	Q₈⋊C₈	C₄×C₅	1	1	yes	characteristic
87	C₈²	C₂²×C₅	1	1	yes	characteristic
88	C₅×Q₈	—	2	1	no	—
89	C₅×Q₈	—	2	1	no	—
90	C₅×Q₈	—	2	1	no	—
91	C₅×Q₈	M₃₂	1	2	yes	—
92	C₂×C₄×C₅	—	2	1	no	—
93	C₂×C₄×C₅	—	2	1	no	—
94	C₂×C₄×C₅	—	2	1	no	—
95	C₂×C₄×C₅	—	2	1	no	—
96	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
97	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
98	C₂×C₄×C₅	#131	1	1	yes	characteristic
99	C₅×C₈	—	2	1	no	—
100	C₅×C₈	—	2	1	no	—
101	C₅×C₈	—	2	1	no	—
102	C₅×C₈	—	4	1	no	—
103	C₅×C₈	—	4	1	no	—
104	C₅×C₈	—	4	1	no	—
105	C₅×C₈	C₂×Q₁₆	1	1	yes	characteristic
106	C₅×C₈	#135	1	1	yes	characteristic
107	C₂×Q₁₆	C₅×C₈	1	1	yes	characteristic
108	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
109	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
110	C₂×C₁₆	—	2	1	no	—
111	C₂×C₁₆	—	2	1	no	—
112	C₂×C₁₆	—	2	1	no	—
113	C₂×C₁₆	C₅×D₄	1	1	yes	characteristic
114	C₂×C₁₆	C₅×D₄	1	1	yes	characteristic
115	#107	C₅×C₈	1	1	yes	characteristic
116	C₄⋊C₈	—	2	1	no	—
117	C₄⋊C₈	—	2	1	no	—
118	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
119	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
120	#103	C₅×C₈	1	1	yes	characteristic
121	#103	C₅×C₈	1	1	yes	characteristic
122	C₄×C₈	—	2	1	no	—
123	C₄×C₈	—	2	1	no	—
124	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
125	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
126	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
127	C₂²×C₅	C₈×D₄	1	1	yes	characteristic
128	C₄×C₅	—	2	2	no	—
129	C₄×C₅	—	2	1	no	—
130	C₄×C₅	—	4	1	no	—
131	C₄×C₅	—	4	1	no	—
132	C₄×C₅	—	4	1	no	—
133	C₄×C₅	C₄×Q₁₆	1	1	yes	characteristic
134	C₄×C₅	#443	1	1	yes	characteristic
135	C₄×C₅	C₂×M₃₂	1	1	yes	characteristic
136	C₄×C₅	#504	1	1	yes	characteristic
137	C₂×Q₈	C₂×C₅×C₈	1	1	yes	characteristic
138	C₂×Q₈	C₂×C₅×C₈	1	1	yes	characteristic
139	Q₁₆	—	2	2	no	—
140	C₂×C₈	—	2	1	no	—
141	C₂×C₈	—	2	1	no	—
142	C₂×C₈	—	2	1	no	—
143	C₂×C₈	C₂×C₅×C₈	1	1	yes	characteristic
144	C₂×C₈	C₂×C₅×C₈	1	1	yes	characteristic
145	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
146	C₂×C₈	C₅×#41	1	1	yes	characteristic
147	C₄⋊C₄	—	2	1	no	—
148	C₄⋊C₄	—	2	1	no	—
149	C₄⋊C₄	C₂×C₅×C₈	1	1	yes	characteristic
150	C₄⋊C₄	C₂×C₅×C₈	1	1	yes	characteristic
151	C₄²	—	2	1	no	—
152	C₄²	—	2	1	no	—
153	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
154	C₁₆	—	2	2	no	—
155	C₁₆	—	2	1	no	—
156	C₁₆	—	4	1	no	—
157	C₁₆	—	4	1	no	—
158	C₁₆	C₅×Q₁₆	1	2	yes	complemented
159	C₂×C₅	C₈×Q₁₆	1	1	yes	characteristic
160	C₂×C₅	#2168	1	1	yes	characteristic
161	C₂×C₅	#2171	1	1	yes	characteristic
162	Q₈	—	2	1	no	—
163	Q₈	—	2	1	no	—
164	Q₈	—	2	1	no	—
165	Q₈	C₅×M₃₂	1	2	yes	—
166	C₂×C₄	—	2	1	no	—
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	2	1	no	—
169	C₂×C₄	—	2	1	no	—
170	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
171	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
172	C₂×C₄	C₅×#131	1	1	yes	characteristic
173	C₈	—	2	1	no	—
174	C₈	—	2	1	no	—
175	C₈	—	2	1	no	—
176	C₈	—	4	1	no	—
177	C₈	—	4	1	no	—
178	C₈	—	4	1	no	—
179	C₈	C₂×C₅×Q₁₆	1	1	yes	characteristic
180	C₈	C₅×#135	1	1	yes	characteristic
181	C₅	#12053	1	1	yes	characteristic, direct product factor, Sylow
182	C₂²	C₅×C₈×D₄	1	1	yes	characteristic
183	C₄	—	2	2	no	—
184	C₄	—	2	1	no	—
185	C₄	—	4	1	no	—
186	C₄	—	4	1	no	—
187	C₄	—	4	1	no	—
188	C₄	C₄×C₅×Q₁₆	1	1	yes	characteristic
189	C₄	C₅×#443	1	1	yes	characteristic
190	C₄	C₂×C₅×M₃₂	1	1	yes	characteristic
191	C₄	C₅×#504	1	1	yes	characteristic
192	C₂	C₅×C₈×Q₁₆	1	1	yes	characteristic
193	C₂	C₅×#2168	1	1	yes	characteristic
194	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, prime radical	C₂²×C₅	C₈×D₄
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
23. #12053	C₅	direct (N × H)
72. C₅×C₁₆	Q₁₆	semidirect
158. C₁₆	C₅×Q₁₆	semidirect
181. C₅	#12053	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×#2183	2
C₅×Q₈×C₁₆	2
C₅×C₈×Q₁₆	2
C₅×#1370	2
C₅×Q₈⋊C₁₆	2
C₅×#1311	2
#12053	5

Subgroups — C5×#12053 #11934773

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#12053 #11934773