Subgroups — D₅×C₃⋊#95 #11748870

Order 960.

660 conjugacy classes of subgroups.

The subgroup lattice has 220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×D₅×Dic₃	C₂	1	2	yes	maximal
3	#91115	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₃⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
5	#90994	C₂	1	2	yes	maximal, complemented
6	D₅×#95	—	3	1	no	maximal, Hall
7	C₂³×C₃×D₅	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂²×Dic₁₅	C₂²	1	2	yes	—
10	C₂²×C₅×Dic₃	C₂²	1	2	yes	—
11	C₂²×C₃×Dic₅	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄×D₅	—	2	4	no	—
13	C₂×C₃×C₄×D₅	C₄	1	4	yes	complemented
14	C₂×D₅×Dic₃	—	2	4	no	—
15	C₂×D₅×Dic₃	—	2	4	no	—
16	C₂×D₅×Dic₃	C₄	1	8	yes	complemented
17	C₂×C₃⋊#95	—	5	1	no	maximal, Hall
18	C₂²×C₄×D₅	—	3	2	no	—
19	C₂²×C₄×D₅	D₃	1	1	yes	characteristic
20	C₅×#95	—	3	1	no	—
21	#3963	—	3	1	no	—
22	#3963	—	3	2	no	—
23	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
24	C₂²×C₃×D₅	C₂×C₄	1	4	yes	—
25	C₂²×C₃×D₅	C₂×C₄	1	2	yes	—
26	C₂²×C₃×D₅	D₄	1	2	yes	—
27	C₂²×C₃×D₅	D₄	1	4	yes	—
28	C₂²×C₃×D₅	Q₈	1	2	yes	—
29	C₂×C₃×C₄×C₅	—	2	2	no	—
30	C₂×C₃×C₄×C₅	C₂×C₄	1	2	yes	complemented
31	C₂×Dic₁₅	—	2	2	no	—
32	C₂×Dic₁₅	—	2	2	no	—
33	C₂×Dic₁₅	C₂×C₄	1	4	yes	complemented
34	C₂×C₅×Dic₃	—	2	2	no	—
35	C₂×C₅×Dic₃	—	2	2	no	—
36	C₂×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
37	C₂×C₃×Dic₅	—	2	2	no	—
38	C₂×C₃×Dic₅	C₂×C₄	1	2	yes	complemented
39	C₃×C₄×D₅	—	2	8	no	—
40	D₅×Dic₃	—	2	16	no	—
41	C₂³×C₃×C₄	—	5	1	no	—
42	C₂³×Dic₃	—	5	2	no	—
43	C₃⋊#95	—	5	1	no	—
44	C₃⋊#95	—	5	2	no	—
45	C₃⋊#95	D₅	1	1	yes	characteristic, direct product factor
46	C₂³×D₅	C₂×D₃	1	1	yes	characteristic
47	C₂²×C₄×C₅	—	3	2	no	—
48	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic
49	C₂²×Dic₅	—	3	2	no	—
50	C₂²×Dic₅	C₂×D₃	1	1	yes	characteristic
51	C₂×C₄×D₅	—	2	4	no	—
52	C₂×C₄×D₅	—	3	8	no	—
53	C₂×C₄×D₅	—	6	4	no	—
54	C₂×C₄×D₅	—	6	4	no	—
55	C₂×C₄×D₅	Dic₃	1	4	yes	complemented
56	C₂×#95	—	15	1	no	Sylow
57	C₂²×C₃×C₅	C₂²×C₄	1	2	yes	—
58	C₂²×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
59	C₂²×C₃×C₅	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₃×C₅	C₂×D₄	1	2	yes	—
61	C₂²×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
62	C₂×C₃×D₅	C₄²	1	4	yes	—
63	C₂×C₃×D₅	C₂²⋊C₄	1	8	yes	—
64	C₂×C₃×D₅	C₂²⋊C₄	1	4	yes	—
65	C₂×C₃×D₅	C₄⋊C₄	1	8	yes	—
66	C₂×C₃×D₅	C₄⋊C₄	1	4	yes	—
67	C₃×C₄×C₅	—	2	2	no	—
68	Dic₁₅	—	2	4	no	—
69	C₃×Dic₅	—	2	2	no	—
70	C₅×Dic₃	—	2	4	no	—
71	C₂⁴×C₃	—	5	1	no	—
72	C₂²×C₃×C₄	—	5	1	no	—
73	C₂²×C₃×C₄	—	5	4	no	—
74	C₂²×C₃×C₄	—	10	4	no	—
75	C₂²×C₃×C₄	C₂×D₅	1	1	yes	characteristic
76	C₂²×Dic₃	—	5	2	no	—
77	C₂²×Dic₃	—	5	8	no	—
78	C₂²×Dic₃	—	10	4	no	—
79	C₂²×Dic₃	—	10	4	no	—
80	C₂²×Dic₃	C₂×D₅	1	2	yes	—
81	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
82	C₂²×D₅	Dic₆	1	2	yes	—
83	C₂²×D₅	C₄×D₃	1	4	yes	—
84	C₂²×D₅	D₁₂	1	2	yes	—
85	C₂²×D₅	C₂×Dic₃	1	2	yes	—
86	C₂²×D₅	#67	1	4	yes	—
87	C₂×C₄×C₅	—	2	2	no	—
88	C₂×C₄×C₅	—	3	4	no	—
89	C₂×C₄×C₅	—	6	2	no	—
90	C₂×C₄×C₅	—	6	2	no	—
91	C₂×C₄×C₅	C₂×Dic₃	1	2	yes	complemented
92	C₂×Dic₅	—	2	2	no	—
93	C₂×Dic₅	—	3	4	no	—
94	C₂×Dic₅	—	6	2	no	—
95	C₂×Dic₅	—	6	2	no	—
96	C₂×Dic₅	C₂×Dic₃	1	2	yes	complemented
97	C₄×D₅	—	2	8	no	—
98	C₄×D₅	—	6	16	no	—
99	C₂³×C₄	—	5	1	no	—
100	C₂³×C₄	—	15	2	no	—
101	#95	—	3	1	no	—
102	#95	—	15	2	no	—
103	#95	—	15	1	no	—
104	C₂×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
105	C₂×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
106	C₂×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
108	C₂×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
109	C₃×D₅	#95	1	8	yes	complemented
110	C₂³×C₃	—	5	4	no	—
111	C₂³×C₃	—	5	2	no	—
112	C₂³×C₃	—	5	2	no	—
113	C₂³×C₃	—	5	4	no	—
114	C₂³×C₃	—	5	2	no	—
115	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
116	C₂×C₃×C₄	—	2	2	no	—
117	C₂×C₃×C₄	—	5	2	no	—
118	C₂×C₃×C₄	—	10	8	no	—
119	C₂×C₃×C₄	—	10	2	no	—
120	C₂×C₃×C₄	C₄×D₅	1	2	yes	complemented
121	C₂×Dic₃	—	2	2	no	—
122	C₂×Dic₃	—	2	2	no	—
123	C₂×Dic₃	—	5	4	no	—
124	C₂×Dic₃	—	10	16	no	—
125	C₂×Dic₃	—	10	2	no	—
126	C₂×Dic₃	—	10	2	no	—
127	C₂×Dic₃	C₄×D₅	1	4	yes	complemented
128	C₂²×C₅	C₂×Dic₆	1	1	yes	characteristic
129	C₂²×C₅	C₂×C₄×D₃	1	2	yes	—
130	C₂²×C₅	C₂×D₁₂	1	1	yes	characteristic
131	C₂²×C₅	C₂²×Dic₃	1	1	yes	characteristic
132	C₂²×C₅	C₂×#67	1	2	yes	—
133	C₂×D₅	C₄×Dic₃	1	4	yes	—
134	C₂×D₅	Dic₃⋊C₄	1	8	yes	—
135	C₂×D₅	C₄⋊Dic₃	1	4	yes	—
136	C₂×D₅	(C₂×D₃)⋊C₄	1	8	yes	—
137	C₂×D₅	#217	1	4	yes	—
138	C₄×C₅	—	2	2	no	—
139	C₄×C₅	—	6	4	no	—
140	Dic₅	—	2	2	no	—
141	Dic₅	—	6	4	no	—
142	C₂⁴	—	5	1	no	—
143	C₂²×C₄	—	3	2	no	—
144	C₂²×C₄	—	5	1	no	—
145	C₂²×C₄	—	5	4	no	—
146	C₂²×C₄	—	10	4	no	—
147	C₂²×C₄	—	15	8	no	—
148	C₂²×C₄	—	15	2	no	—
149	C₂²×C₄	—	30	4	no	—
150	C₂²×C₄	—	30	4	no	—
151	C₂²×C₄	D₃×D₅	1	1	yes	characteristic
152	C₃×C₅	C₂×#95	1	1	yes	characteristic, complemented, Hall
153	C₂²×C₃	—	5	4	no	—
154	C₂²×C₃	—	5	8	no	—
155	C₂²×C₃	—	5	4	no	—
156	C₂²×C₃	—	5	8	no	—
157	C₂²×C₃	—	5	4	no	—
158	C₂²×C₃	C₂×C₄×D₅	1	2	yes	—
159	C₂²×C₃	C₂×C₄×D₅	1	1	yes	characteristic
160	C₂²×C₃	D₄×D₅	1	1	yes	characteristic
161	C₂²×C₃	D₄×D₅	1	2	yes	—
162	C₂²×C₃	Q₈×D₅	1	1	yes	characteristic
163	C₃×C₄	—	2	2	no	—
164	C₃×C₄	—	10	2	no	—
165	Dic₃	—	2	4	no	—
166	Dic₃	—	10	4	no	—
167	C₂×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
168	C₂×C₅	C₂×Dic₃⋊C₄	1	2	yes	—
169	C₂×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
170	C₂×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
171	C₂×C₅	C₂×#217	1	1	yes	characteristic
172	D₅	C₃⋊#95	1	8	yes	direct product factor
173	C₂³	—	5	2	no	—
174	C₂³	—	5	4	no	—
175	C₂³	—	5	2	no	—
176	C₂³	—	5	2	no	—
177	C₂³	—	5	4	no	—
178	C₂³	C₂×D₃×D₅	1	1	yes	characteristic
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	3	4	no	—
181	C₂×C₄	—	5	2	no	—
182	C₂×C₄	—	6	2	no	—
183	C₂×C₄	—	6	2	no	—
184	C₂×C₄	—	10	8	no	—
185	C₂×C₄	—	10	2	no	—
186	C₂×C₄	—	15	4	no	—
187	C₂×C₄	—	30	16	no	—
188	C₂×C₄	—	30	2	no	—
189	C₂×C₄	—	30	2	no	—
190	C₂×C₄	D₅×Dic₃	1	2	yes	complemented
191	C₂×C₃	—	5	8	no	—
192	C₂×C₃	C₄²×D₅	1	1	yes	characteristic
193	C₂×C₃	D₅×C₂²⋊C₄	1	2	yes	—
194	C₂×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₃	D₅×C₄⋊C₄	1	2	yes	—
196	C₂×C₃	D₅×C₄⋊C₄	1	1	yes	characteristic
197	C₅	C₂×C₃⋊#95	1	1	yes	characteristic, complemented, Sylow
198	C₂²	—	5	8	no	—
199	C₂²	—	5	4	no	—
200	C₂²	—	5	8	no	—
201	C₂²	—	5	4	no	—
202	C₂²	—	5	4	no	—
203	C₂²	D₅×Dic₆	1	1	yes	characteristic
204	C₂²	C₄×D₃×D₅	1	2	yes	—
205	C₂²	D₅×D₁₂	1	1	yes	characteristic
206	C₂²	C₂×D₅×Dic₃	1	1	yes	characteristic
207	C₂²	D₅×#67	1	2	yes	—
208	C₄	—	2	2	no	—
209	C₄	—	6	4	no	—
210	C₄	—	10	2	no	—
211	C₄	—	30	4	no	—
212	C₃	D₅×#95	1	1	yes	characteristic, complemented, Sylow
213	C₂	—	5	8	no	—
214	C₂	C₄×D₅×Dic₃	1	1	yes	characteristic
215	C₂	D₅×Dic₃⋊C₄	1	2	yes	—
216	C₂	D₅×C₄⋊Dic₃	1	1	yes	characteristic
217	C₂	D₅×(C₂×D₃)⋊C₄	1	2	yes	—
218	C₂	D₅×#217	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂×D₃×D₅
commutator	C₂×C₃×C₅	C₂×C₄²
Fitting	C₂²×C₃×C₄×C₅	C₂²
socle, cosocle	C₂³×C₃×C₅	C₂³
prime radical	C₂³×C₃×D₅	C₂²
hypercenter	C₂²×C₄	D₃×D₅
hypocenter	C₃×C₅	C₂×#95
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
3. #91115	C₂	semidirect
4. C₅×C₃⋊#95	C₂	semidirect
5. #90994	C₂	semidirect
13. C₂×C₃×C₄×D₅	C₄	semidirect
16. C₂×D₅×Dic₃	C₄	semidirect
30. C₂×C₃×C₄×C₅	C₂×C₄	semidirect
33. C₂×Dic₁₅	C₂×C₄	semidirect
36. C₂×C₅×Dic₃	C₂×C₄	semidirect
38. C₂×C₃×Dic₅	C₂×C₄	semidirect
45. C₃⋊#95	D₅	direct (N × H)
55. C₂×C₄×D₅	Dic₃	semidirect
91. C₂×C₄×C₅	C₂×Dic₃	semidirect
96. C₂×Dic₅	C₂×Dic₃	semidirect
109. C₃×D₅	#95	semidirect
120. C₂×C₃×C₄	C₄×D₅	semidirect
127. C₂×Dic₃	C₄×D₅	semidirect
152. C₃×C₅	C₂×#95	semidirect
172. D₅	C₃⋊#95	direct (N × H)
190. C₂×C₄	D₅×Dic₃	semidirect
197. C₅	C₂×C₃⋊#95	semidirect
212. C₃	D₅×#95	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄×D₅	2
C₂²×D₅×Dic₃	2
#91115	2
C₅×C₃⋊#95	2
#90994	2
D₅×#95	3
C₂×C₃⋊#95	5

Subgroups — D5×C3⋊#95 #11748870

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₃⋊#95 #11748870