Subgroups — C₅×#21737 #11944457

Order 1280.

662 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3162	C₂	1	1	yes	maximal, characteristic
2	C₅×#2960	C₂	1	2	yes	maximal
3	C₅×#1995	C₂	1	2	yes	maximal
4	C₅×#1945	C₂	1	4	yes	maximal
5	C₅×#1849	C₂	1	1	yes	maximal, characteristic
6	C₅×#1773	C₂	1	4	yes	maximal
7	C₅×#1726	C₂	1	1	yes	maximal, characteristic
8	C₅×#533	C₂²	1	2	yes	—
9	C₅×#501	C₄	1	8	yes	complemented
10	C₅×#446	—	2	4	no	—
11	C₅×C₈×Q₈	—	2	4	no	—
12	C₂×C₅×#108	C₂²	1	4	yes	—
13	C₅×#427	C₂²	1	4	yes	—
14	C₅×#424	C₂²	1	4	yes	—
15	C₅×#423	C₂²	1	2	yes	—
16	C₅×#405	C₂²	1	4	yes	—
17	C₂×C₅×#97	C₂²	1	1	yes	characteristic
18	C₂×C₅×#97	C₂²	1	2	yes	—
19	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
20	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₅×#376	C₂²	1	1	yes	characteristic
22	C₅×#339	C₂²	1	8	yes	—
23	#21737	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂×C₅×M₁₆	C₂³	1	4	yes	—
25	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
26	C₂²×C₅×C₈	C₂³	1	2	yes	—
27	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
28	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	—
29	C₅×#125	C₂×C₄	1	4	yes	—
30	C₅×C₂²⋊Q₈	—	2	4	no	—
31	C₄×C₅×Q₈	—	2	4	no	—
32	C₅×#117	C₂³	1	4	yes	—
33	C₂×C₄²×C₅	C₂³	1	2	yes	—
34	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
35	C₅×#108	—	2	8	no	—
36	C₅×#107	C₂×C₄	1	8	yes	—
37	C₅×#106	C₂×C₄	1	8	yes	—
38	C₅×C₄⋊C₈	—	2	8	no	—
39	C₅×C₄⋊C₈	—	2	4	no	—
40	C₅×#97	—	2	4	no	—
41	C₅×#97	C₂×C₄	1	4	yes	—
42	C₅×#97	Q₈	1	8	yes	complemented
43	C₄×C₅×C₈	—	2	4	no	—
44	C₄×C₅×C₈	—	2	4	no	—
45	C₄×C₅×C₈	D₄	1	4	yes	—
46	C₅×#95	—	2	2	no	—
47	#3162	C₂×C₅	1	1	yes	characteristic
48	#2960	C₂×C₅	1	2	yes	—
49	#1995	C₂×C₅	1	2	yes	—
50	#1945	C₂×C₅	1	4	yes	—
51	#1849	C₂×C₅	1	1	yes	characteristic
52	#1773	C₂×C₅	1	4	yes	—
53	#1726	C₂×C₅	1	1	yes	characteristic
54	C₂×C₅×Q₈	—	2	4	no	—
55	C₂²×C₄×C₅	—	2	2	no	—
56	C₂²×C₄×C₅	#41	1	2	yes	—
57	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
58	C₅×M₁₆	—	2	8	no	—
59	C₂×C₅×C₈	—	2	2	no	—
60	C₂×C₅×C₈	—	2	4	no	—
61	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
62	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
63	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
64	C₂×C₅×C₈	C₂×Q₈	1	4	yes	—
65	C₂×C₅×C₈	C₂×Q₈	1	4	yes	—
66	C₂×C₅×C₈	#41	1	4	yes	—
67	C₅×C₄⋊C₄	—	2	8	no	—
68	C₅×C₄⋊C₄	—	2	4	no	—
69	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
70	C₅×C₂²⋊C₄	—	2	4	no	—
71	C₄²×C₅	—	2	4	no	—
72	C₄²×C₅	—	2	2	no	—
73	C₄²×C₅	C₂²×C₄	1	2	yes	—
74	C₄²×C₅	C₂×D₄	1	2	yes	—
75	C₄²×C₅	C₂×Q₈	1	4	yes	—
76	#533	C₂²×C₅	1	2	yes	—
77	#501	C₄×C₅	1	8	yes	complemented
78	#446	—	2	4	no	—
79	C₈×Q₈	—	2	4	no	—
80	C₂×#108	C₂²×C₅	1	4	yes	—
81	#427	C₂²×C₅	1	4	yes	—
82	#424	C₂²×C₅	1	4	yes	—
83	#423	C₂²×C₅	1	2	yes	—
84	#405	C₂²×C₅	1	4	yes	—
85	C₂×#97	C₂²×C₅	1	1	yes	characteristic
86	C₂×#97	C₂²×C₅	1	2	yes	—
87	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
88	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
89	#376	C₂²×C₅	1	1	yes	characteristic
90	#339	C₂²×C₅	1	8	yes	—
91	C₂³×C₅	C₂×#41	1	1	yes	characteristic
92	C₅×Q₈	—	4	8	no	—
93	C₂×C₄×C₅	—	2	8	no	—
94	C₂×C₄×C₅	—	2	4	no	—
95	C₂×C₄×C₅	—	4	2	no	—
96	C₂×C₄×C₅	—	4	4	no	—
97	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
98	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
99	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
100	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
101	C₂×C₄×C₅	C₂×#41	1	2	yes	—
102	C₅×C₈	—	2	2	no	—
103	C₅×C₈	—	4	4	no	—
104	C₅×C₈	C₄×Q₈	1	8	yes	—
105	C₅×C₈	C₄⋊Q₈	1	4	yes	—
106	C₂×M₁₆	C₂³×C₅	1	4	yes	—
107	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
108	C₂²×C₈	C₂³×C₅	1	2	yes	—
109	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
110	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	—
111	#125	C₂×C₄×C₅	1	4	yes	—
112	C₂²⋊Q₈	—	2	4	no	—
113	C₄×Q₈	—	2	4	no	—
114	#117	C₂³×C₅	1	4	yes	—
115	C₂×C₄²	C₂³×C₅	1	2	yes	—
116	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
117	#108	—	2	8	no	—
118	#107	C₂×C₄×C₅	1	8	yes	—
119	#106	C₂×C₄×C₅	1	8	yes	—
120	C₄⋊C₈	—	2	8	no	—
121	C₄⋊C₈	—	2	4	no	—
122	#97	—	2	4	no	—
123	#97	C₂×C₄×C₅	1	4	yes	—
124	#97	C₅×Q₈	1	8	yes	complemented
125	C₄×C₈	—	2	4	no	—
126	C₄×C₈	—	2	4	no	—
127	C₄×C₈	C₅×D₄	1	4	yes	—
128	#95	—	2	2	no	—
129	C₂²×C₅	—	2	2	no	—
130	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
131	C₂²×C₅	#533	1	2	yes	—
132	C₄×C₅	—	2	4	no	—
133	C₄×C₅	—	4	4	no	—
134	C₄×C₅	—	4	8	no	—
135	C₄×C₅	C₂×C₄×Q₈	1	2	yes	—
136	C₄×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
137	C₄×C₅	#532	1	1	yes	characteristic
138	C₂×Q₈	—	2	4	no	—
139	C₂²×C₄	—	2	2	no	—
140	C₂²×C₄	C₅×#41	1	2	yes	—
141	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
142	M₁₆	—	2	8	no	—
143	C₂×C₈	—	2	2	no	—
144	C₂×C₈	—	2	4	no	—
145	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
146	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
147	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
148	C₂×C₈	C₂×C₅×Q₈	1	4	yes	—
149	C₂×C₈	C₂×C₅×Q₈	1	4	yes	—
150	C₂×C₈	C₅×#41	1	4	yes	—
151	C₄⋊C₄	—	2	8	no	—
152	C₄⋊C₄	—	2	4	no	—
153	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
154	C₂²⋊C₄	—	2	4	no	—
155	C₄²	—	2	4	no	—
156	C₄²	—	2	2	no	—
157	C₄²	C₂²×C₄×C₅	1	2	yes	—
158	C₄²	C₂×C₅×D₄	1	2	yes	—
159	C₄²	C₂×C₅×Q₈	1	4	yes	—
160	C₂×C₅	—	2	2	no	—
161	C₂×C₅	C₄×C₄⋊Q₈	1	1	yes	characteristic
162	C₂×C₅	#2955	1	2	yes	—
163	C₂³	C₂×C₅×#41	1	1	yes	characteristic
164	Q₈	—	4	8	no	—
165	C₂×C₄	—	2	8	no	—
166	C₂×C₄	—	2	4	no	—
167	C₂×C₄	—	4	2	no	—
168	C₂×C₄	—	4	4	no	—
169	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
170	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
171	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
172	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
173	C₂×C₄	C₂×C₅×#41	1	2	yes	—
174	C₈	—	2	2	no	—
175	C₈	—	4	4	no	—
176	C₈	C₄×C₅×Q₈	1	8	yes	—
177	C₈	C₅×C₄⋊Q₈	1	4	yes	—
178	C₅	#21737	1	1	yes	characteristic, direct product factor, Sylow
179	C₂²	—	2	2	no	—
180	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
181	C₂²	C₅×#533	1	2	yes	—
182	C₄	—	2	4	no	—
183	C₄	—	4	4	no	—
184	C₄	—	4	8	no	—
185	C₄	C₂×C₄×C₅×Q₈	1	2	yes	—
186	C₄	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
187	C₄	C₅×#532	1	1	yes	characteristic
188	C₂	—	2	2	no	—
189	C₂	C₄×C₅×C₄⋊Q₈	1	1	yes	characteristic
190	C₂	C₅×#2955	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂³×C₅	C₂×#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
9. C₅×#501	C₄	semidirect
23. #21737	C₅	direct (N × H)
42. C₅×#97	Q₈	semidirect
77. #501	C₄×C₅	semidirect
124. #97	C₅×Q₈	semidirect
178. C₅	#21737	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×#3162	2
C₅×#2960	2
C₅×#1995	2
C₅×#1945	2
C₅×#1849	2
C₅×#1773	2
C₅×#1726	2
#21737	5

Subgroups — C5×#21737 #11944457

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21737 #11944457