Subgroups — C₅×#9623 #11932343

Order 1280.

298 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#1950	C₂	1	2	yes	maximal
2	C₅×#1566	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#334	C₂	1	1	yes	maximal, characteristic
4	C₅×C₈×M₁₆	C₂	1	1	yes	maximal, characteristic
5	C₅×#1301	C₂	1	2	yes	maximal
6	C₅×#431	C₂²	1	1	yes	characteristic
7	C₂×C₅×#108	—	2	2	no	—
8	C₅×#423	C₂²	1	2	yes	—
9	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
10	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₅×#341	—	2	2	no	—
13	C₅×#334	—	2	1	no	—
14	C₅×#334	—	2	1	no	—
15	C₅×#334	C₄	1	2	yes	—
16	C₅×#334	C₄	1	2	yes	—
17	C₅×#322	—	2	1	no	—
18	C₅×C₈²	—	2	1	no	—
19	#9623	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂×C₅×M₁₆	—	2	2	no	—
21	C₂×C₅×M₁₆	D₄	1	2	yes	—
22	C₂²×C₅×C₈	—	2	2	no	—
23	C₂²×C₅×C₈	Q₈	1	1	yes	characteristic
24	C₂²×C₅×C₈	Q₈	1	1	yes	characteristic
25	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
26	C₅×#108	—	4	4	no	—
27	C₅×C₄⋊C₈	—	2	2	no	—
28	C₅×C₄⋊C₈	—	2	2	no	—
29	C₅×C₄⋊C₈	—	2	1	no	—
30	C₅×C₄⋊C₈	—	2	2	no	—
31	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
32	C₅×C₂²⋊C₈	Q₈	1	2	yes	—
33	C₅×#97	—	2	1	no	—
34	C₄×C₅×C₈	—	2	1	no	—
35	C₄×C₅×C₈	—	2	1	no	—
36	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
37	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
38	C₄×C₅×C₈	D₄	1	1	yes	characteristic
39	C₄×C₅×C₈	D₄	1	1	yes	characteristic
40	#1950	C₂×C₅	1	2	yes	—
41	#1566	C₂×C₅	1	1	yes	characteristic
42	C₂×#334	C₂×C₅	1	1	yes	characteristic
43	C₈×M₁₆	C₂×C₅	1	1	yes	characteristic
44	#1301	C₂×C₅	1	2	yes	—
45	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
47	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
48	C₅×M₁₆	—	2	2	no	—
49	C₅×M₁₆	—	4	2	no	—
50	C₅×M₁₆	—	4	2	no	—
51	C₅×M₁₆	SD₁₆	1	4	yes	—
52	C₂×C₅×C₈	—	2	2	no	—
53	C₂×C₅×C₈	—	2	2	no	—
54	C₂×C₅×C₈	—	2	4	no	—
55	C₂×C₅×C₈	—	2	2	no	—
56	C₂×C₅×C₈	—	4	1	no	—
57	C₂×C₅×C₈	—	4	2	no	—
58	C₂×C₅×C₈	—	4	2	no	—
59	C₂×C₅×C₈	—	4	2	no	—
60	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
62	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
64	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
65	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₅	#41	1	1	yes	characteristic
67	C₄²×C₅	#41	1	1	yes	characteristic
68	#431	C₂²×C₅	1	1	yes	characteristic
69	C₂×#108	—	2	2	no	—
70	#423	C₂²×C₅	1	2	yes	—
71	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
72	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
73	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
74	#341	—	2	2	no	—
75	#334	—	2	1	no	—
76	#334	—	2	1	no	—
77	#334	C₄×C₅	1	2	yes	—
78	#334	C₄×C₅	1	2	yes	—
79	#322	—	2	1	no	—
80	C₈²	—	2	1	no	—
81	C₂³×C₅	C₄⋊Q₈	1	1	yes	characteristic
82	C₂×C₄×C₅	—	2	1	no	—
83	C₂×C₄×C₅	—	2	1	no	—
84	C₂×C₄×C₅	—	4	1	no	—
85	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
87	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
88	C₂×C₄×C₅	#121	1	1	yes	characteristic
89	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
90	C₂×C₄×C₅	#125	1	1	yes	characteristic
91	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
92	C₂×C₄×C₅	#135	1	2	yes	—
93	C₅×C₈	—	2	1	no	—
94	C₅×C₈	—	2	1	no	—
95	C₅×C₈	—	2	1	no	—
96	C₅×C₈	—	2	4	no	—
97	C₅×C₈	—	4	2	no	—
98	C₅×C₈	—	4	4	no	—
99	C₅×C₈	—	8	2	no	—
100	C₅×C₈	#108	1	2	yes	complemented
101	C₂×M₁₆	—	2	2	no	—
102	C₂×M₁₆	C₅×D₄	1	2	yes	—
103	C₂²×C₈	—	2	2	no	—
104	C₂²×C₈	C₅×Q₈	1	1	yes	characteristic
105	C₂²×C₈	C₅×Q₈	1	1	yes	characteristic
106	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
107	#108	—	4	4	no	—
108	C₄⋊C₈	—	2	2	no	—
109	C₄⋊C₈	—	2	2	no	—
110	C₄⋊C₈	—	2	1	no	—
111	C₄⋊C₈	—	2	2	no	—
112	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
113	C₂²⋊C₈	C₅×Q₈	1	2	yes	—
114	#97	—	2	1	no	—
115	C₄×C₈	—	2	1	no	—
116	C₄×C₈	—	2	1	no	—
117	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
118	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
119	C₄×C₈	C₅×D₄	1	1	yes	characteristic
120	C₄×C₈	C₅×D₄	1	1	yes	characteristic
121	C₂²×C₅	—	2	1	no	—
122	C₂²×C₅	—	2	1	no	—
123	C₂²×C₅	#389	1	1	yes	characteristic
124	C₂²×C₅	#498	1	1	yes	characteristic
125	C₂²×C₅	#499	1	1	yes	characteristic
126	C₄×C₅	—	2	1	no	—
127	C₄×C₅	—	2	1	no	—
128	C₄×C₅	—	2	1	no	—
129	C₄×C₅	C₂×#108	1	1	yes	characteristic
130	C₄×C₅	#430	1	1	yes	characteristic
131	C₄×C₅	C₄×SD₁₆	1	2	yes	—
132	C₄×C₅	#465	1	2	yes	—
133	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
134	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
135	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
136	M₁₆	—	2	2	no	—
137	M₁₆	—	4	2	no	—
138	M₁₆	—	4	2	no	—
139	M₁₆	C₅×SD₁₆	1	4	yes	—
140	C₂×C₈	—	2	2	no	—
141	C₂×C₈	—	2	2	no	—
142	C₂×C₈	—	2	4	no	—
143	C₂×C₈	—	2	2	no	—
144	C₂×C₈	—	4	1	no	—
145	C₂×C₈	—	4	2	no	—
146	C₂×C₈	—	4	2	no	—
147	C₂×C₈	—	4	2	no	—
148	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
152	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
153	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
154	C₄²	C₅×#41	1	1	yes	characteristic
155	C₄²	C₅×#41	1	1	yes	characteristic
156	C₂×C₅	—	2	1	no	—
157	C₂×C₅	—	2	1	no	—
158	C₂×C₅	#1941	1	1	yes	characteristic
159	C₂×C₅	#1950	1	1	yes	characteristic
160	C₂×C₅	#1953	1	1	yes	characteristic
161	C₂³	C₅×C₄⋊Q₈	1	1	yes	characteristic
162	C₂×C₄	—	2	1	no	—
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	4	1	no	—
165	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
167	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
168	C₂×C₄	C₅×#121	1	1	yes	characteristic
169	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
170	C₂×C₄	C₅×#125	1	1	yes	characteristic
171	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
172	C₂×C₄	C₅×#135	1	2	yes	—
173	C₈	—	2	1	no	—
174	C₈	—	2	1	no	—
175	C₈	—	2	1	no	—
176	C₈	—	2	4	no	—
177	C₈	—	4	2	no	—
178	C₈	—	4	4	no	—
179	C₈	—	8	2	no	—
180	C₈	C₅×#108	1	2	yes	complemented
181	C₅	#9623	1	1	yes	characteristic, direct product factor, Sylow
182	C₂²	—	2	1	no	—
183	C₂²	—	2	1	no	—
184	C₂²	C₅×#389	1	1	yes	characteristic
185	C₂²	C₅×#498	1	1	yes	characteristic
186	C₂²	C₅×#499	1	1	yes	characteristic
187	C₄	—	2	1	no	—
188	C₄	—	2	1	no	—
189	C₄	—	2	1	no	—
190	C₄	C₂×C₅×#108	1	1	yes	characteristic
191	C₄	C₅×#430	1	1	yes	characteristic
192	C₄	C₄×C₅×SD₁₆	1	2	yes	—
193	C₄	C₅×#465	1	2	yes	—
194	C₂	—	2	1	no	—
195	C₂	—	2	1	no	—
196	C₂	C₅×#1941	1	1	yes	characteristic
197	C₂	C₅×#1950	1	1	yes	characteristic
198	C₂	C₅×#1953	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	#121
commutator	C₄²	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
socle	C₂²×C₅	#389
prime radical	C₂³×C₅	C₄⋊Q₈
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
19. #9623	C₅	direct (N × H)
100. C₅×C₈	#108	semidirect
180. C₈	C₅×#108	semidirect
181. C₅	#9623	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×#1950	2
C₅×#1566	2
C₂×C₅×#334	2
C₅×C₈×M₁₆	2
C₅×#1301	2
#9623	5

Subgroups — C5×#9623 #11932343

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#9623 #11932343