Subgroups — C₂×D₁₃×M₃₂ #13127930

Order 1664.

400 conjugacy classes of subgroups.

The subgroup lattice has 176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#88052	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×M₃₂	C₂	1	8	yes	maximal, direct product factor
5	C₂×#88038	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₆×D₁₃	C₂	1	2	yes	maximal, complemented
7	C₂²×C₄×D₁₃	C₄	1	1	yes	characteristic
8	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂²×#1055	C₄	1	1	yes	characteristic
10	C₂×C₈×D₁₃	C₄	1	4	yes	—
11	C₂×C₈×D₁₃	C₄	1	1	yes	characteristic
12	C₂×C₈×D₁₃	C₄	1	1	yes	characteristic
13	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₈×D₁₃	C₂²	1	4	yes	—
16	C₁₃×M₃₂	C₂²	1	4	yes	complemented
17	C₂×C₁₃×C₁₆	C₂²	1	2	yes	complemented
18	#88052	C₂²	1	4	yes	complemented
19	C₂×#6090	C₂²	1	2	yes	complemented
20	#88038	C₂²	1	8	yes	complemented
21	C₁₆×D₁₃	C₂²	1	8	yes	complemented
22	C₂³×D₁₃	C₈	1	1	yes	characteristic
23	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×Dic₁₃	C₈	1	1	yes	characteristic
25	C₂×C₄×D₁₃	C₈	1	1	yes	characteristic
26	C₂×C₄×D₁₃	C₈	1	4	yes	—
27	C₂×C₄×D₁₃	C₈	1	1	yes	characteristic
28	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×D₁₃	C₂×C₄	1	4	yes	—
30	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
33	C₂×C₈×C₁₃	C₂³	1	2	yes	—
34	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
35	C₂×#1055	C₂×C₄	1	1	yes	characteristic
36	C₂×#1055	C₂×C₄	1	1	yes	characteristic
37	C₂×#1055	C₂×C₄	1	4	yes	—
38	C₈×D₁₃	C₂×C₄	1	2	yes	—
39	C₈×D₁₃	C₂×C₄	1	2	yes	—
40	C₈×D₁₃	C₂×C₄	1	4	yes	—
41	C₈×D₁₃	C₂×C₄	1	4	yes	—
42	C₈×D₁₃	C₂³	1	2	yes	—
43	C₈×D₁₃	C₂³	1	2	yes	—
44	C₁₃×C₁₆	C₂³	1	4	yes	complemented
45	#6090	C₂³	1	4	yes	complemented
46	C₂²×M₃₂	—	13	1	no	maximal, Sylow
47	C₂³×C₁₃	C₂×C₈	1	1	yes	characteristic
48	C₂²×D₁₃	—	2	4	no	—
49	C₂²×D₁₃	C₂×C₈	1	1	yes	characteristic
50	C₂²×D₁₃	C₂×C₈	1	4	yes	—
51	C₂²×D₁₃	C₂×C₈	1	1	yes	characteristic
52	C₂×C₄×C₁₃	C₂×C₈	1	2	yes	—
53	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
54	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
55	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
56	C₂×Dic₁₃	C₂×C₈	1	4	yes	—
57	C₂×Dic₁₃	C₂×C₈	1	1	yes	characteristic
58	C₂×Dic₁₃	C₂×C₈	1	1	yes	characteristic
59	C₄×D₁₃	C₂×C₈	1	2	yes	—
60	C₄×D₁₃	C₂×C₈	1	4	yes	—
61	C₄×D₁₃	C₂×C₈	1	2	yes	—
62	C₄×D₁₃	C₂×C₈	1	4	yes	—
63	C₄×D₁₃	C₂²×C₄	1	2	yes	—
64	C₄×D₁₃	C₂²×C₄	1	2	yes	—
65	C₈×C₁₃	C₂²×C₄	1	2	yes	—
66	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
67	C₈×C₁₃	C₂⁴	1	1	yes	characteristic
68	#1055	C₂²×C₄	1	2	yes	—
69	#1055	C₂²×C₄	1	2	yes	—
70	C₂³×C₈	—	13	1	no	—
71	C₂×M₃₂	—	13	1	no	—
72	C₂×M₃₂	—	13	8	no	—
73	C₂×M₃₂	—	13	2	no	—
74	C₂×M₃₂	D₁₃	1	1	yes	characteristic, direct product factor
75	C₂²×C₁₆	—	13	2	no	—
76	C₂²×C₁₃	—	2	2	no	—
77	C₂²×C₁₃	C₂²×C₈	1	2	yes	—
78	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
79	C₂×D₁₃	—	2	2	no	—
80	C₂×D₁₃	—	2	8	no	—
81	C₂×D₁₃	M₃₂	1	4	yes	direct product factor
82	C₂×D₁₃	C₂²×C₈	1	2	yes	—
83	C₂×D₁₃	C₂²×C₈	1	2	yes	—
84	C₄×C₁₃	C₂²×C₈	1	2	yes	—
85	C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
86	C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
87	Dic₁₃	C₂²×C₈	1	2	yes	—
88	Dic₁₃	C₂²×C₈	1	2	yes	—
89	C₂³×C₄	—	13	1	no	—
90	C₂²×C₈	—	13	1	no	—
91	C₂²×C₈	—	13	4	no	—
92	C₂²×C₈	—	13	1	no	—
93	C₂²×C₈	—	13	1	no	—
94	C₂²×C₈	—	13	4	no	—
95	C₂²×C₈	—	13	1	no	—
96	C₂²×C₈	—	13	1	no	—
97	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
98	M₃₂	—	13	4	no	—
99	M₃₂	—	13	8	no	—
100	M₃₂	C₂×D₁₃	1	4	yes	direct product factor
101	C₂×C₁₆	—	13	2	no	—
102	C₂×C₁₆	—	13	8	no	—
103	C₂×C₁₆	C₂×D₁₃	1	2	yes	complemented
104	C₂×C₁₃	—	2	2	no	—
105	C₂×C₁₃	C₂×M₃₂	1	2	yes	complemented
106	C₂×C₁₃	C₂³×C₈	1	1	yes	characteristic
107	D₁₃	—	2	2	no	—
108	D₁₃	C₂×M₃₂	1	4	yes	direct product factor
109	C₂⁴	—	13	1	no	—
110	C₂²×C₄	—	13	1	no	—
111	C₂²×C₄	—	13	1	no	—
112	C₂²×C₄	—	13	4	no	—
113	C₂²×C₄	—	13	1	no	—
114	C₂²×C₄	—	13	4	no	—
115	C₂²×C₄	—	13	1	no	—
116	C₂²×C₄	—	13	1	no	—
117	C₂²×C₄	C₄×D₁₃	1	1	yes	characteristic
118	C₂×C₈	—	13	4	no	—
119	C₂×C₈	—	13	1	no	—
120	C₂×C₈	—	13	1	no	—
121	C₂×C₈	—	13	4	no	—
122	C₂×C₈	—	13	4	no	—
123	C₂×C₈	—	13	2	no	—
124	C₂×C₈	—	13	2	no	—
125	C₂×C₈	—	13	2	no	—
126	C₂×C₈	—	13	2	no	—
127	C₂×C₈	C₄×D₁₃	1	1	yes	characteristic
128	C₂×C₈	C₄×D₁₃	1	2	yes	—
129	C₂×C₈	C₂²×D₁₃	1	2	yes	—
130	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
131	C₁₆	—	13	4	no	—
132	C₁₆	C₂²×D₁₃	1	4	yes	complemented
133	C₁₃	C₂²×M₃₂	1	1	yes	characteristic, complemented, Sylow
134	C₂³	—	13	1	no	—
135	C₂³	—	13	4	no	—
136	C₂³	—	13	1	no	—
137	C₂³	—	26	4	no	—
138	C₂³	C₈×D₁₃	1	1	yes	characteristic
139	C₂×C₄	—	13	4	no	—
140	C₂×C₄	—	13	1	no	—
141	C₂×C₄	—	13	1	no	—
142	C₂×C₄	—	13	4	no	—
143	C₂×C₄	—	13	2	no	—
144	C₂×C₄	—	13	4	no	—
145	C₂×C₄	—	13	2	no	—
146	C₂×C₄	—	13	2	no	—
147	C₂×C₄	—	13	2	no	—
148	C₂×C₄	C₈×D₁₃	1	2	yes	—
149	C₂×C₄	C₈×D₁₃	1	1	yes	characteristic
150	C₂×C₄	C₂×C₄×D₁₃	1	2	yes	—
151	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
152	C₈	—	13	2	no	—
153	C₈	—	13	2	no	—
154	C₈	C₂×C₄×D₁₃	1	2	yes	—
155	C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
156	C₈	C₂³×D₁₃	1	1	yes	characteristic
157	C₂²	—	2	2	no	—
158	C₂²	—	13	2	no	—
159	C₂²	—	13	4	no	—
160	C₂²	—	13	2	no	—
161	C₂²	—	26	8	no	—
162	C₂²	—	26	2	no	—
163	C₂²	C₂×C₈×D₁₃	1	2	yes	—
164	C₂²	C₂×C₈×D₁₃	1	1	yes	characteristic
165	C₄	—	13	2	no	—
166	C₄	—	13	2	no	—
167	C₄	C₂×C₈×D₁₃	1	2	yes	—
168	C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
169	C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
170	C₂	—	2	2	no	—
171	C₂	—	13	4	no	—
172	C₂	—	26	2	no	—
173	C₂	D₁₃×M₃₂	1	2	yes	direct product factor
174	C₂	C₂²×C₈×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×D₁₃
commutator	C₂×C₁₃	C₂³×C₈
Frattini	C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×M₃₂	C₂
socle	C₂²×C₁₃	C₂²×C₈
prime radical	C₂³×D₁₃	C₈
cosocle	C₈×C₁₃	C₂⁴
hypercenter	C₂×M₃₂	D₁₃
hypocenter	C₁₃	C₂²×M₃₂
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×M₃₂	C₂	semidirect
3. C₂×#88052	C₂	semidirect
4. D₁₃×M₃₂	C₂	direct (N × H)
5. C₂×#88038	C₂	semidirect
6. C₂×C₁₆×D₁₃	C₂	semidirect
16. C₁₃×M₃₂	C₂²	semidirect
17. C₂×C₁₃×C₁₆	C₂²	semidirect
18. #88052	C₂²	semidirect
19. C₂×#6090	C₂²	semidirect
20. #88038	C₂²	semidirect
21. C₁₆×D₁₃	C₂²	semidirect
44. C₁₃×C₁₆	C₂³	semidirect
45. #6090	C₂³	semidirect
74. C₂×M₃₂	D₁₃	direct (N × H)
81. C₂×D₁₃	M₃₂	direct (N × H)
100. M₃₂	C₂×D₁₃	direct (N × H)
103. C₂×C₁₆	C₂×D₁₃	semidirect
105. C₂×C₁₃	C₂×M₃₂	semidirect
108. D₁₃	C₂×M₃₂	direct (N × H)
132. C₁₆	C₂²×D₁₃	semidirect
133. C₁₃	C₂²×M₃₂	semidirect
173. C₂	D₁₃×M₃₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₈×D₁₃	2
C₂×C₁₃×M₃₂	2
C₂×#88052	2
D₁₃×M₃₂	2
C₂×#88038	2
C₂×C₁₆×D₁₃	2
C₂²×M₃₂	13

Subgroups — C2×D13×M32 #13127930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃×M₃₂ #13127930