Subgroups — C₃×#10602214 #14314363

Order 1920.

320 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₃×#65390	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×#672	C₂	1	1	yes	maximal, characteristic
4	C₃×#64721	C₂	1	4	yes	maximal, complemented
5	#10602214	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₃×#4072	C₄	1	1	yes	characteristic
8	C₂×C₃×#681	C₄	1	1	yes	characteristic
9	C₃×C₅×M₃₂	—	2	2	no	—
10	C₂×C₃×C₅×C₁₆	C₂²	1	2	yes	—
11	C₃×#3947	C₄	1	2	yes	—
12	C₃×C₈×Dic₅	C₂²	1	2	yes	—
13	C₂×C₃×#672	—	2	2	no	—
14	C₂×C₃×#672	C₂²	1	2	yes	—
15	C₃×#2151	—	5	1	no	maximal, Hall
16	C₂×C₅×M₃₂	C₂×C₃	1	1	yes	characteristic
17	#65390	C₂×C₃	1	1	yes	characteristic
18	C₂²×#672	C₂×C₃	1	1	yes	characteristic
19	#64721	C₂×C₃	1	4	yes	complemented
20	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
21	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
22	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
23	C₂×C₃×C₅×C₈	Q₈	1	2	yes	—
24	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
25	C₃×C₂²⋊Dic₅	C₈	1	2	yes	—
26	C₃×C₄⋊Dic₅	C₈	1	2	yes	—
27	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
28	C₃×#681	—	2	2	no	—
29	C₂×C₃×#168	C₂×C₄	1	2	yes	—
30	C₃×C₅×C₁₆	—	2	2	no	—
31	C₃×#672	—	2	2	no	—
32	C₂×C₃×M₃₂	D₅	1	1	yes	characteristic
33	C₂²×C₃×C₁₆	—	5	1	no	—
34	C₃×#405	—	5	1	no	—
35	C₃×C₄⋊C₁₆	—	5	4	no	—
36	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
37	#4072	C₃×C₄	1	1	yes	characteristic
38	C₂×#681	C₃×C₄	1	1	yes	characteristic
39	C₅×M₃₂	—	2	2	no	—
40	C₂×C₅×C₁₆	C₂²×C₃	1	2	yes	—
41	#3947	C₃×C₄	1	2	yes	—
42	C₈×Dic₅	C₂²×C₃	1	2	yes	—
43	C₂×#672	—	2	2	no	—
44	C₂×#672	C₂²×C₃	1	2	yes	—
45	#2151	—	5	1	no	Sylow
46	C₂³×C₃×C₅	C₂×C₈	1	1	yes	characteristic
47	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
48	C₂×C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
49	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
50	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₃×Dic₅	C₂×C₈	1	4	yes	—
52	C₃×C₅×C₈	C₄⋊C₄	1	2	yes	—
53	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
54	C₃×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
55	C₃×#168	—	2	2	no	—
56	C₂×C₃×M₁₆	—	5	1	no	—
57	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
58	C₃×#117	—	5	1	no	—
59	C₃×M₃₂	—	2	2	no	—
60	C₂×C₃×C₁₆	—	5	2	no	—
61	C₂×C₃×C₁₆	—	10	2	no	—
62	C₂×C₃×C₁₆	C₂×D₅	1	2	yes	—
63	C₃×#97	—	5	2	no	—
64	C₃×C₄×C₈	—	5	2	no	—
65	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
66	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
67	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
68	C₂×C₅×C₈	C₃×Q₈	1	2	yes	—
69	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
70	C₂²⋊Dic₅	C₃×C₈	1	2	yes	—
71	C₄⋊Dic₅	C₃×C₈	1	2	yes	—
72	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
73	#681	—	2	2	no	—
74	C₂×#168	C₂×C₃×C₄	1	2	yes	—
75	C₅×C₁₆	—	2	2	no	—
76	#672	—	2	2	no	—
77	C₂×M₃₂	C₃×D₅	1	1	yes	characteristic
78	C₂²×C₁₆	—	5	1	no	—
79	#405	—	5	1	no	—
80	C₄⋊C₁₆	—	5	4	no	—
81	C₂²×C₃×C₅	—	2	2	no	—
82	C₂²×C₃×C₅	C₄⋊C₈	1	2	yes	—
83	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
84	C₃×C₄×C₅	C₄⋊C₈	1	2	yes	—
85	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
86	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
87	C₃×Dic₅	—	2	4	no	—
88	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
89	C₃×M₁₆	—	10	2	no	—
90	C₂×C₃×C₈	—	5	2	no	—
91	C₂×C₃×C₈	Dic₁₀	1	2	yes	—
92	C₂×C₃×C₈	C₄×D₅	1	1	yes	characteristic
93	C₂×C₃×C₈	C₂²⋊D₅	1	2	yes	—
94	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
95	C₃×C₄⋊C₄	—	5	2	no	—
96	C₃×C₂²⋊C₄	—	5	2	no	—
97	C₃×C₄²	—	5	2	no	—
98	C₃×C₁₆	—	2	2	no	—
99	C₃×C₁₆	—	10	2	no	—
100	C₂³×C₅	C₂×C₃×C₈	1	1	yes	characteristic
101	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
102	C₂×C₄×C₅	C₂×C₃×C₈	1	1	yes	characteristic
103	C₂×C₄×C₅	C₃×M₁₆	1	2	yes	—
104	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
105	C₂×Dic₅	C₂×C₃×C₈	1	4	yes	—
106	C₅×C₈	C₃×C₄⋊C₄	1	2	yes	—
107	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
108	C₅×C₈	C₂×C₃×Q₈	1	1	yes	characteristic
109	#168	—	2	2	no	—
110	C₂×M₁₆	—	5	1	no	—
111	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
112	#117	—	5	1	no	—
113	M₃₂	—	2	2	no	—
114	C₂×C₁₆	—	5	2	no	—
115	C₂×C₁₆	—	10	2	no	—
116	C₂×C₁₆	C₂×C₃×D₅	1	2	yes	—
117	#97	—	5	2	no	—
118	C₄×C₈	—	5	2	no	—
119	C₂×C₃×C₅	—	2	2	no	—
120	C₂×C₃×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
121	C₂×C₃×C₅	#504	1	2	yes	—
122	C₂³×C₃	C₈×D₅	1	1	yes	characteristic
123	C₂×C₃×C₄	—	5	4	no	—
124	C₂×C₃×C₄	C₈×D₅	1	1	yes	characteristic
125	C₂×C₃×C₄	#676	1	2	yes	—
126	C₂×C₃×C₄	#683	1	2	yes	—
127	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
128	C₃×C₈	—	10	2	no	—
129	C₃×C₈	#683	1	2	yes	—
130	C₃×C₈	C₂×Dic₁₀	1	1	yes	characteristic
131	C₃×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
132	C₂²×C₅	—	2	2	no	—
133	C₂²×C₅	C₃×C₄⋊C₈	1	2	yes	—
134	C₂²×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
135	C₄×C₅	C₃×C₄⋊C₈	1	2	yes	—
136	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
137	C₄×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
138	Dic₅	—	2	4	no	—
139	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
140	M₁₆	—	10	2	no	—
141	C₂×C₈	—	5	2	no	—
142	C₂×C₈	C₃×Dic₁₀	1	2	yes	—
143	C₂×C₈	C₃×C₄×D₅	1	1	yes	characteristic
144	C₂×C₈	C₃×C₂²⋊D₅	1	2	yes	—
145	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
146	C₄⋊C₄	—	5	2	no	—
147	C₂²⋊C₄	—	5	2	no	—
148	C₄²	—	5	2	no	—
149	C₁₆	—	2	2	no	—
150	C₁₆	—	10	2	no	—
151	C₃×C₅	#2151	1	1	yes	characteristic, complemented, Hall
152	C₂²×C₃	—	2	2	no	—
153	C₂²×C₃	#3946	1	2	yes	—
154	C₂²×C₃	C₂×C₈×D₅	1	1	yes	characteristic
155	C₃×C₄	—	10	4	no	—
156	C₃×C₄	#3946	1	2	yes	—
157	C₃×C₄	C₂×#676	1	1	yes	characteristic
158	C₃×C₄	C₂×#683	1	1	yes	characteristic
159	C₂×C₅	—	2	2	no	—
160	C₂×C₅	C₂×C₃×C₄⋊C₈	1	1	yes	characteristic
161	C₂×C₅	C₃×#504	1	2	yes	—
162	C₂³	C₃×C₈×D₅	1	1	yes	characteristic
163	C₂×C₄	—	5	4	no	—
164	C₂×C₄	C₃×C₈×D₅	1	1	yes	characteristic
165	C₂×C₄	C₃×#676	1	2	yes	—
166	C₂×C₄	C₃×#683	1	2	yes	—
167	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
168	C₈	—	10	2	no	—
169	C₈	C₃×#683	1	2	yes	—
170	C₈	C₂×C₃×Dic₁₀	1	1	yes	characteristic
171	C₈	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
172	C₂×C₃	—	2	2	no	—
173	C₂×C₃	#65196	1	2	yes	—
174	C₂×C₃	C₂×#3946	1	1	yes	characteristic
175	C₅	C₃×#2151	1	1	yes	characteristic, complemented, Sylow
176	C₂²	—	2	2	no	—
177	C₂²	C₃×#3946	1	2	yes	—
178	C₂²	C₂×C₃×C₈×D₅	1	1	yes	characteristic
179	C₄	—	10	4	no	—
180	C₄	C₃×#3946	1	2	yes	—
181	C₄	C₂×C₃×#676	1	1	yes	characteristic
182	C₄	C₂×C₃×#683	1	1	yes	characteristic
183	C₃	#10602214	1	1	yes	characteristic, direct product factor, Sylow
184	C₂	—	2	2	no	—
185	C₂	C₃×#65196	1	2	yes	—
186	C₂	C₂×C₃×#3946	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₈	C₂²×D₅
commutator	C₂²×C₅	C₂²×C₃×C₈
Frattini	C₂×C₈	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×M₃₂	C₂
socle	C₂²×C₃×C₅	C₂²×C₈
prime radical	C₂³×C₃×C₅	C₂×C₈
cosocle	C₂×C₅×C₈	C₂³×C₃
hypercenter	C₂×C₃×M₃₂	D₅
hypocenter	C₅	C₃×#2151
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₈ ◁ C₂×C₃×M₃₂

Complements

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

N	H ≅ G/N	type
4. C₃×#64721	C₂	semidirect
5. #10602214	C₃	direct (N × H)
19. #64721	C₂×C₃	semidirect
151. C₃×C₅	#2151	semidirect
175. C₅	C₃×#2151	semidirect
183. C₃	#10602214	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×M₃₂	2
C₃×#65390	2
C₂²×C₃×#672	2
C₃×#64721	2
#10602214	3
C₃×#2151	5

Subgroups — C3×#10602214 #14314363

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10602214 #14314363