Subgroups — C₃×C₅×#479 #11751454

Order 960.

180 conjugacy classes of subgroups.

The subgroup lattice has 172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#106	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic
8	C₅×#479	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₅×C₄⋊C₄	—	2	1	no	—
13	C₃×C₅×C₄⋊C₄	—	2	1	no	—
14	C₃×C₅×C₄⋊C₄	—	2	1	no	—
15	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₃×C₄²×C₅	—	2	1	no	—
19	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
20	C₃×#479	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₅×#125	C₂×C₃	1	1	yes	characteristic
22	C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic
23	C₅×#107	C₂×C₃	1	1	yes	characteristic
24	C₅×#106	C₂×C₃	1	1	yes	characteristic
25	C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
26	C₅×#103	C₂×C₃	1	1	yes	characteristic
27	C₅×#103	C₂×C₃	1	1	yes	characteristic
28	C₃×C₅×Q₈	—	2	1	no	—
29	C₃×C₅×Q₈	Q₈	1	2	yes	—
30	C₂×C₃×C₄×C₅	—	2	1	no	—
31	C₂×C₃×C₄×C₅	—	2	1	no	—
32	C₂×C₃×C₄×C₅	—	2	1	no	—
33	C₂×C₃×C₄×C₅	—	2	1	no	—
34	C₂×C₃×C₄×C₅	D₄	1	1	yes	characteristic
35	C₂×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₃×C₅×C₈	—	2	1	no	—
38	C₃×C₅×C₈	—	2	1	no	—
39	C₃×#125	C₂×C₅	1	1	yes	characteristic
40	C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic
41	C₃×#107	C₂×C₅	1	1	yes	characteristic
42	C₃×#106	C₂×C₅	1	1	yes	characteristic
43	C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
44	C₃×#103	C₂×C₅	1	1	yes	characteristic
45	C₃×#103	C₂×C₅	1	1	yes	characteristic
46	C₂×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
47	C₂×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
48	C₂×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
49	C₅×C₄⋊C₄	—	2	1	no	—
50	C₅×C₄⋊C₄	—	2	1	no	—
51	C₅×C₄⋊C₄	—	2	1	no	—
52	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
53	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
54	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
55	C₄²×C₅	—	2	1	no	—
56	C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
57	#479	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
58	C₂²×C₃×C₅	C₂×D₄	1	1	yes	characteristic
59	C₃×C₄×C₅	—	2	2	no	—
60	C₃×C₄×C₅	—	2	1	no	—
61	C₃×C₄×C₅	—	2	1	no	—
62	C₃×C₄×C₅	—	4	1	no	—
63	C₃×C₄×C₅	—	4	1	no	—
64	C₃×C₄×C₅	—	4	1	no	—
65	C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
66	C₃×C₄×C₅	#41	1	1	yes	characteristic
67	C₂×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
68	C₂×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
69	C₂×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
70	C₃×C₄⋊C₄	—	2	1	no	—
71	C₃×C₄⋊C₄	—	2	1	no	—
72	C₃×C₄⋊C₄	—	2	1	no	—
73	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
74	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
75	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
76	C₃×C₄²	—	2	1	no	—
77	C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
78	C₅×Q₈	—	2	1	no	—
79	C₅×Q₈	C₃×Q₈	1	2	yes	—
80	C₂×C₄×C₅	—	2	1	no	—
81	C₂×C₄×C₅	—	2	1	no	—
82	C₂×C₄×C₅	—	2	1	no	—
83	C₂×C₄×C₅	—	2	1	no	—
84	C₂×C₄×C₅	C₃×D₄	1	1	yes	characteristic
85	C₂×C₄×C₅	C₃×D₄	1	1	yes	characteristic
86	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
87	C₅×C₈	—	2	1	no	—
88	C₅×C₈	—	2	1	no	—
89	#125	C₂×C₃×C₅	1	1	yes	characteristic
90	C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
91	#107	C₂×C₃×C₅	1	1	yes	characteristic
92	#106	C₂×C₃×C₅	1	1	yes	characteristic
93	C₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic
94	#103	C₂×C₃×C₅	1	1	yes	characteristic
95	#103	C₂×C₃×C₅	1	1	yes	characteristic
96	C₂×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
97	C₂×C₃×C₅	#135	1	1	yes	characteristic
98	C₂×C₃×C₅	#137	1	1	yes	characteristic
99	C₃×Q₈	—	2	1	no	—
100	C₃×Q₈	C₅×Q₈	1	2	yes	—
101	C₂×C₃×C₄	—	2	1	no	—
102	C₂×C₃×C₄	—	2	1	no	—
103	C₂×C₃×C₄	—	2	1	no	—
104	C₂×C₃×C₄	—	2	1	no	—
105	C₂×C₃×C₄	C₅×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄	C₅×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
108	C₃×C₈	—	2	1	no	—
109	C₃×C₈	—	2	1	no	—
110	C₂²×C₅	C₂×C₃×D₄	1	1	yes	characteristic
111	C₄×C₅	—	2	2	no	—
112	C₄×C₅	—	2	1	no	—
113	C₄×C₅	—	2	1	no	—
114	C₄×C₅	—	4	1	no	—
115	C₄×C₅	—	4	1	no	—
116	C₄×C₅	—	4	1	no	—
117	C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
118	C₄×C₅	C₃×#41	1	1	yes	characteristic
119	C₂×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
120	C₂×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
121	C₂×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
122	C₄⋊C₄	—	2	1	no	—
123	C₄⋊C₄	—	2	1	no	—
124	C₄⋊C₄	—	2	1	no	—
125	C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
126	C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
127	C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
128	C₄²	—	2	1	no	—
129	C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
130	C₃×C₅	#479	1	1	yes	characteristic, direct product factor, Hall
131	C₂²×C₃	C₂×C₅×D₄	1	1	yes	characteristic
132	C₃×C₄	—	2	2	no	—
133	C₃×C₄	—	2	1	no	—
134	C₃×C₄	—	2	1	no	—
135	C₃×C₄	—	4	1	no	—
136	C₃×C₄	—	4	1	no	—
137	C₃×C₄	—	4	1	no	—
138	C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
139	C₃×C₄	C₅×#41	1	1	yes	characteristic
140	C₂×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
141	C₂×C₅	C₃×#135	1	1	yes	characteristic
142	C₂×C₅	C₃×#137	1	1	yes	characteristic
143	Q₈	—	2	1	no	—
144	Q₈	C₃×C₅×Q₈	1	2	yes	—
145	C₂×C₄	—	2	1	no	—
146	C₂×C₄	—	2	1	no	—
147	C₂×C₄	—	2	1	no	—
148	C₂×C₄	—	2	1	no	—
149	C₂×C₄	C₃×C₅×D₄	1	1	yes	characteristic
150	C₂×C₄	C₃×C₅×D₄	1	1	yes	characteristic
151	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
152	C₈	—	2	1	no	—
153	C₈	—	2	1	no	—
154	C₂×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
155	C₂×C₃	C₅×#135	1	1	yes	characteristic
156	C₂×C₃	C₅×#137	1	1	yes	characteristic
157	C₅	C₃×#479	1	1	yes	characteristic, direct product factor, Sylow
158	C₂²	C₂×C₃×C₅×D₄	1	1	yes	characteristic
159	C₄	—	2	2	no	—
160	C₄	—	2	1	no	—
161	C₄	—	2	1	no	—
162	C₄	—	4	1	no	—
163	C₄	—	4	1	no	—
164	C₄	—	4	1	no	—
165	C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
166	C₄	C₃×C₅×#41	1	1	yes	characteristic
167	C₃	C₅×#479	1	1	yes	characteristic, direct product factor, Sylow
168	C₂	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
169	C₂	C₃×C₅×#135	1	1	yes	characteristic
170	C₂	C₃×C₅×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₅×#479	C₃	direct (N × H)
20. C₃×#479	C₅	direct (N × H)
57. #479	C₃×C₅	direct (N × H)
130. C₃×C₅	#479	direct (N × H)
157. C₅	C₃×#479	direct (N × H)
167. C₃	C₅×#479	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#125	2
C₃×C₄×C₅×Q₈	2
C₃×C₅×#107	2
C₃×C₅×#106	2
C₃×C₅×C₄⋊C₈	2
C₃×C₅×#103	2
C₅×#479	3
C₃×#479	5

Subgroups — C3×C5×#479 #11751454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#479 #11751454