Subgroups — C₁₃×#13640 #15699979

Order 3328.

194 conjugacy classes of subgroups.

The subgroup lattice has 154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₄⋊C₃₂	C₂	1	2	yes	maximal, complemented
3	C₁₃×C₂²⋊C₃₂	C₂	1	2	yes	maximal
4	C₁₃×#1397	C₂	1	2	yes	maximal, complemented
5	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic
6	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
8	C₂×C₁₃×C₃₂	C₂²	1	4	yes	—
9	C₄×C₁₃×C₁₆	C₄	1	1	yes	characteristic
10	C₄×C₁₃×C₁₆	C₄	1	1	yes	characteristic
11	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
12	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₁₃	C₈	1	1	yes	characteristic
14	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄²×C₁₃	C₈	1	1	yes	characteristic
16	C₂×C₁₃×C₁₆	—	2	2	no	—
17	C₂×C₁₃×C₁₆	—	2	2	no	—
18	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
20	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
21	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
22	C₄×C₈×C₁₃	C₈	1	1	yes	characteristic
23	C₄×C₈×C₁₃	C₈	1	1	yes	characteristic
24	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₁₃×C₃₂	—	2	4	no	—
27	#13640	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂²×C₄×C₁₃	C₁₆	1	1	yes	characteristic
29	C₂²×C₄×C₁₃	C₁₆	1	1	yes	characteristic
30	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
31	C₂×C₈×C₁₃	—	2	2	no	—
32	C₂×C₈×C₁₃	—	2	1	no	—
33	C₂×C₈×C₁₃	—	2	1	no	—
34	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
35	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
36	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
37	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
38	C₄²×C₁₃	C₁₆	1	1	yes	characteristic
39	C₄²×C₁₃	C₁₆	1	1	yes	characteristic
40	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
41	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
42	C₁₃×C₁₆	—	2	1	no	—
43	C₁₃×C₁₆	—	2	1	no	—
44	C₁₃×C₁₆	M₁₆	1	2	yes	—
45	C₁₃×C₁₆	#41	1	2	yes	—
46	C₂×C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic
47	C₄⋊C₃₂	C₂×C₁₃	1	2	yes	complemented
48	C₂²⋊C₃₂	C₂×C₁₃	1	2	yes	—
49	#1397	C₂×C₁₃	1	2	yes	complemented
50	C₂³×C₁₃	C₂×C₁₆	1	1	yes	characteristic
51	C₂×C₄×C₁₃	—	2	2	no	—
52	C₂×C₄×C₁₃	—	2	2	no	—
53	C₂×C₄×C₁₃	—	2	1	no	—
54	C₂×C₄×C₁₃	—	2	1	no	—
55	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
56	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
57	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
58	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
59	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
60	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
61	C₈×C₁₃	—	2	1	no	—
62	C₈×C₁₃	—	2	1	no	—
63	C₈×C₁₃	M₃₂	1	2	yes	—
64	C₈×C₁₃	#117	1	1	yes	characteristic
65	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
66	C₂²×C₁₆	C₄×C₁₃	1	1	yes	characteristic
67	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
68	C₂×C₄×C₈	C₄×C₁₃	1	1	yes	characteristic
69	C₂×C₃₂	C₂²×C₁₃	1	4	yes	—
70	C₄×C₁₆	C₄×C₁₃	1	1	yes	characteristic
71	C₄×C₁₆	C₄×C₁₃	1	1	yes	characteristic
72	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
73	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
74	C₂²×C₁₃	—	2	1	no	—
75	C₂²×C₁₃	—	2	1	no	—
76	C₂²×C₁₃	M₆₄	1	2	yes	—
77	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
78	C₄×C₁₃	—	2	1	no	—
79	C₄×C₁₃	—	2	1	no	—
80	C₄×C₁₃	—	2	1	no	—
81	C₄×C₁₃	—	2	1	no	—
82	C₄×C₁₃	M₆₄	1	2	yes	—
83	C₄×C₁₃	#431	1	1	yes	characteristic
84	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
85	C₂²×C₈	C₈×C₁₃	1	1	yes	characteristic
86	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
87	C₂×C₄²	C₈×C₁₃	1	1	yes	characteristic
88	C₂×C₁₆	—	2	2	no	—
89	C₂×C₁₆	—	2	2	no	—
90	C₂×C₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
91	C₂×C₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
92	C₂×C₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
93	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
94	C₄×C₈	C₈×C₁₃	1	1	yes	characteristic
95	C₄×C₈	C₈×C₁₃	1	1	yes	characteristic
96	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
97	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
98	C₃₂	—	2	4	no	—
99	C₂×C₁₃	—	2	2	no	—
100	C₂×C₁₃	#2162	1	1	yes	characteristic
101	C₂×C₁₃	C₂×M₆₄	1	1	yes	characteristic
102	C₂×C₁₃	C₂×M₆₄	1	1	yes	characteristic
103	C₂²×C₄	C₁₃×C₁₆	1	1	yes	characteristic
104	C₂²×C₄	C₁₃×C₁₆	1	1	yes	characteristic
105	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
106	C₂×C₈	—	2	2	no	—
107	C₂×C₈	—	2	1	no	—
108	C₂×C₈	—	2	1	no	—
109	C₂×C₈	C₂×C₈×C₁₃	1	1	yes	characteristic
110	C₂×C₈	C₂×C₈×C₁₃	1	1	yes	characteristic
111	C₂×C₈	C₂×C₈×C₁₃	1	1	yes	characteristic
112	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
113	C₄²	C₁₃×C₁₆	1	1	yes	characteristic
114	C₄²	C₁₃×C₁₆	1	1	yes	characteristic
115	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
116	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
117	C₁₆	—	2	1	no	—
118	C₁₆	—	2	1	no	—
119	C₁₆	C₁₃×M₁₆	1	2	yes	—
120	C₁₆	C₁₃×#41	1	2	yes	—
121	C₁₃	#13640	1	1	yes	characteristic, direct product factor, Sylow
122	C₂³	C₂×C₁₃×C₁₆	1	1	yes	characteristic
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	2	2	no	—
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	C₂×C₁₃×C₁₆	1	1	yes	characteristic
128	C₂×C₄	C₂×C₁₃×C₁₆	1	1	yes	characteristic
129	C₂×C₄	C₂×C₁₃×C₁₆	1	1	yes	characteristic
130	C₂×C₄	C₂×C₁₃×C₁₆	1	1	yes	characteristic
131	C₂×C₄	C₂×C₁₃×C₁₆	1	1	yes	characteristic
132	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
133	C₈	—	2	1	no	—
134	C₈	—	2	1	no	—
135	C₈	C₁₃×M₃₂	1	2	yes	—
136	C₈	C₁₃×#117	1	1	yes	characteristic
137	C₈	C₂×C₁₃×M₁₆	1	1	yes	characteristic
138	C₂²	—	2	1	no	—
139	C₂²	—	2	1	no	—
140	C₂²	C₁₃×M₆₄	1	2	yes	—
141	C₂²	C₂²×C₁₃×C₁₆	1	1	yes	characteristic
142	C₄	—	2	1	no	—
143	C₄	—	2	1	no	—
144	C₄	—	2	1	no	—
145	C₄	—	2	1	no	—
146	C₄	C₁₃×M₆₄	1	2	yes	—
147	C₄	C₁₃×#431	1	1	yes	characteristic
148	C₄	C₂×C₁₃×M₃₂	1	1	yes	characteristic
149	C₂	—	2	2	no	—
150	C₂	C₁₃×#2162	1	1	yes	characteristic
151	C₂	C₂×C₁₃×M₆₄	1	1	yes	characteristic
152	C₂	C₂×C₁₃×M₆₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₃×C₁₆	C₂³
commutator	C₂²	C₂²×C₁₃×C₁₆
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
socle	C₂²×C₁₃	C₂²×C₁₆
prime radical	C₂³×C₁₃	C₂×C₁₆
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₁₃×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×C₄⋊C₃₂	C₂	semidirect
4. C₁₃×#1397	C₂	semidirect
27. #13640	C₁₃	direct (N × H)
47. C₄⋊C₃₂	C₂×C₁₃	semidirect
49. #1397	C₂×C₁₃	semidirect
121. C₁₃	#13640	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×C₄×C₁₃×C₁₆	2
C₁₃×C₄⋊C₃₂	2
C₁₃×C₂²⋊C₃₂	2
C₁₃×#1397	2
#13640	13

Subgroups — C13×#13640 #15699979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13640 #15699979