Subgroups — C₅×#68929 #14298913

Order 1920.

360 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×#5118	C₂	1	2	yes	maximal
2	C₂×C₅×#815	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#341	C₂	1	1	yes	maximal, characteristic
4	C₅×#4558	C₂	1	2	yes	maximal
5	C₅×#4552	C₂	1	1	yes	maximal, characteristic
6	C₅×#1838	—	3	1	no	maximal, Hall
7	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
8	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
10	C₂×C₅×#208	C₂²	1	2	yes	—
11	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
12	C₅×#815	C₄	1	4	yes	—
13	C₅×Dic₃⋊C₈	—	2	4	no	—
14	#68929	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₅×#423	—	3	2	no	—
16	C₂×C₅×#97	—	3	1	no	—
17	C₅×#341	—	3	2	no	—
18	C₅×#341	—	3	1	no	—
19	C₅×#341	D₃	1	1	yes	characteristic
20	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
21	C₂²×C₅×Dic₃	Q₈	1	2	yes	—
22	C₃×C₅×M₁₆	—	2	2	no	—
23	C₃×C₅×M₁₆	—	2	2	no	—
24	C₂×C₃×C₅×C₈	—	2	2	no	—
25	C₂×C₃×C₅×C₈	—	2	2	no	—
26	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
27	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
28	C₄×C₅×Dic₃	D₄	1	2	yes	—
29	C₅×#208	—	2	2	no	—
30	C₅×#208	—	2	2	no	—
31	C₂×C₅×C₃⋊C₈	—	2	2	no	—
32	C₂×C₅×C₃⋊C₈	—	2	2	no	—
33	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
34	#5118	C₂×C₅	1	2	yes	—
35	C₂×#815	C₂×C₅	1	1	yes	characteristic
36	C₃×#341	C₂×C₅	1	1	yes	characteristic
37	#4558	C₂×C₅	1	2	yes	—
38	#4552	C₂×C₅	1	1	yes	characteristic
39	C₂×C₅×M₁₆	—	3	2	no	—
40	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	—
41	C₂²×C₅×C₈	—	3	1	no	—
42	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
43	C₂×C₄²×C₅	—	3	1	no	—
44	C₅×C₄⋊C₈	—	6	4	no	—
45	C₅×#97	—	3	4	no	—
46	#1838	—	3	1	no	Sylow
47	C₂³×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
50	C₂×C₃×C₄×C₅	#41	1	2	yes	—
51	C₂×C₃×C₄×C₅	#41	1	2	yes	—
52	C₂×C₅×Dic₃	—	4	2	no	—
53	C₂×C₅×Dic₃	C₄⋊C₄	1	4	yes	—
54	C₃×C₅×C₈	—	2	2	no	—
55	C₃×C₅×C₈	—	4	2	no	—
56	C₅×C₃⋊C₈	—	2	2	no	—
57	C₅×C₃⋊C₈	—	4	2	no	—
58	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
59	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
60	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
61	C₂×#208	C₂²×C₅	1	2	yes	—
62	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
63	#815	C₄×C₅	1	4	yes	—
64	Dic₃⋊C₈	—	2	4	no	—
65	C₂²×C₄×C₅	—	3	2	no	—
66	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
67	C₅×M₁₆	—	2	2	no	—
68	C₅×M₁₆	—	2	2	no	—
69	C₅×M₁₆	—	6	2	no	—
70	C₅×M₁₆	—	6	2	no	—
71	C₂×C₅×C₈	—	2	2	no	—
72	C₂×C₅×C₈	—	2	2	no	—
73	C₂×C₅×C₈	—	3	2	no	—
74	C₂×C₅×C₈	—	6	2	no	—
75	C₂×C₅×C₈	—	6	2	no	—
76	C₂×C₅×C₈	C₄×D₃	1	2	yes	—
77	C₄²×C₅	—	3	2	no	—
78	C₄²×C₅	—	3	2	no	—
79	#423	—	3	2	no	—
80	C₂×#97	—	3	1	no	—
81	#341	—	3	2	no	—
82	#341	—	3	1	no	—
83	#341	C₅×D₃	1	1	yes	characteristic
84	C₂²×C₃×C₅	—	2	2	no	—
85	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₃×C₅	#125	1	2	yes	—
87	C₃×C₄×C₅	#117	1	1	yes	characteristic
88	C₃×C₄×C₅	#117	1	1	yes	characteristic
89	C₃×C₄×C₅	#124	1	2	yes	—
90	C₅×Dic₃	—	2	4	no	—
91	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
92	C₂²×Dic₃	C₅×Q₈	1	2	yes	—
93	C₃×M₁₆	—	2	2	no	—
94	C₃×M₁₆	—	2	2	no	—
95	C₂×C₃×C₈	—	2	2	no	—
96	C₂×C₃×C₈	—	2	2	no	—
97	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
98	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
99	C₄×Dic₃	C₅×D₄	1	2	yes	—
100	#208	—	2	2	no	—
101	#208	—	2	2	no	—
102	C₂×C₃⋊C₈	—	2	2	no	—
103	C₂×C₃⋊C₈	—	2	2	no	—
104	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
105	C₂³×C₅	D₃×Q₈	1	1	yes	characteristic
106	C₂×C₄×C₅	—	3	4	no	—
107	C₂×C₄×C₅	—	12	2	no	—
108	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
109	C₂×C₄×C₅	#235	1	2	yes	—
110	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
111	C₂×C₄×C₅	#237	1	2	yes	—
112	C₅×C₈	—	2	2	no	—
113	C₅×C₈	—	4	2	no	—
114	C₅×C₈	—	6	2	no	—
115	C₅×C₈	—	12	2	no	—
116	C₂×M₁₆	—	3	2	no	—
117	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	—
118	C₂²×C₈	—	3	1	no	—
119	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
120	C₂×C₄²	—	3	1	no	—
121	C₄⋊C₈	—	6	4	no	—
122	#97	—	3	4	no	—
123	C₂×C₃×C₅	—	2	2	no	—
124	C₂×C₃×C₅	#382	1	1	yes	characteristic
125	C₂×C₃×C₅	#430	1	2	yes	—
126	C₂³×C₃	C₂×C₅×Q₈	1	1	yes	characteristic
127	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
128	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
129	C₂×C₃×C₄	C₅×#41	1	2	yes	—
130	C₂×C₃×C₄	C₅×#41	1	2	yes	—
131	C₂×Dic₃	—	4	2	no	—
132	C₂×Dic₃	C₅×C₄⋊C₄	1	4	yes	—
133	C₃×C₈	—	2	2	no	—
134	C₃×C₈	—	4	2	no	—
135	C₃⋊C₈	—	2	2	no	—
136	C₃⋊C₈	—	4	2	no	—
137	C₂²×C₅	—	2	2	no	—
138	C₂²×C₅	#889	1	2	yes	—
139	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
140	C₄×C₅	—	6	4	no	—
141	C₄×C₅	#872	1	1	yes	characteristic
142	C₄×C₅	#877	1	1	yes	characteristic
143	C₄×C₅	#885	1	2	yes	—
144	C₂²×C₄	—	3	2	no	—
145	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
146	M₁₆	—	2	2	no	—
147	M₁₆	—	2	2	no	—
148	M₁₆	—	6	2	no	—
149	M₁₆	—	6	2	no	—
150	C₂×C₈	—	2	2	no	—
151	C₂×C₈	—	2	2	no	—
152	C₂×C₈	—	3	2	no	—
153	C₂×C₈	—	6	2	no	—
154	C₂×C₈	—	6	2	no	—
155	C₂×C₈	C₄×C₅×D₃	1	2	yes	—
156	C₄²	—	3	2	no	—
157	C₄²	—	3	2	no	—
158	C₃×C₅	#1838	1	1	yes	characteristic, complemented, Hall
159	C₂²×C₃	—	2	2	no	—
160	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
161	C₂²×C₃	C₅×#125	1	2	yes	—
162	C₃×C₄	C₅×#117	1	1	yes	characteristic
163	C₃×C₄	C₅×#117	1	1	yes	characteristic
164	C₃×C₄	C₅×#124	1	2	yes	—
165	Dic₃	—	2	4	no	—
166	C₂×C₅	—	2	2	no	—
167	C₂×C₅	#4650	1	1	yes	characteristic
168	C₂×C₅	#4893	1	2	yes	—
169	C₂³	C₅×D₃×Q₈	1	1	yes	characteristic
170	C₂×C₄	—	3	4	no	—
171	C₂×C₄	—	12	2	no	—
172	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
173	C₂×C₄	C₅×#235	1	2	yes	—
174	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
175	C₂×C₄	C₅×#237	1	2	yes	—
176	C₈	—	2	2	no	—
177	C₈	—	4	2	no	—
178	C₈	—	6	2	no	—
179	C₈	—	12	2	no	—
180	C₂×C₃	—	2	2	no	—
181	C₂×C₃	C₅×#382	1	1	yes	characteristic
182	C₂×C₃	C₅×#430	1	2	yes	—
183	C₅	#68929	1	1	yes	characteristic, direct product factor, Sylow
184	C₂²	—	2	2	no	—
185	C₂²	C₅×#889	1	2	yes	—
186	C₂²	C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
187	C₄	—	6	4	no	—
188	C₄	C₅×#872	1	1	yes	characteristic
189	C₄	C₅×#877	1	1	yes	characteristic
190	C₄	C₅×#885	1	2	yes	—
191	C₃	C₅×#1838	1	1	yes	characteristic, complemented, Sylow
192	C₂	—	2	2	no	—
193	C₂	C₅×#4650	1	1	yes	characteristic
194	C₂	C₅×#4893	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#341	C₂
socle	C₂²×C₃×C₅	C₂×C₄⋊C₄
prime radical	C₂³×C₃×C₅	C₂×Q₈
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#341	D₃
hypocenter	C₃	C₅×#1838
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#341

Complements

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

N	H ≅ G/N	type
14. #68929	C₅	direct (N × H)
158. C₃×C₅	#1838	semidirect
183. C₅	#68929	direct (N × H)
191. C₃	C₅×#1838	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5118	2
C₂×C₅×#815	2
C₃×C₅×#341	2
C₅×#4558	2
C₅×#4552	2
C₅×#1838	3
#68929	5

Subgroups — C5×#68929 #14298913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68929 #14298913