Subgroups — C₁₃×#13641 #15699980

Order 3328.

180 conjugacy classes of subgroups.

The subgroup lattice has 140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2108	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	1	yes	maximal, characteristic, complemented
5	C₄×C₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×M₃₂	C₄	1	1	yes	characteristic
7	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₁₃×#405	C₄	1	1	yes	characteristic
9	C₂×C₁₃×C₃₂	C₂²	1	2	yes	—
10	C₂×C₁₃×C₃₂	C₂²	1	2	yes	—
11	C₁₃×#346	C₄	1	1	yes	characteristic
12	C₁₃×#346	C₄	1	1	yes	characteristic
13	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×M₁₆	C₈	1	1	yes	characteristic
16	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₁₃×#117	C₈	1	1	yes	characteristic
18	C₁₃×M₃₂	—	2	2	no	—
19	C₂×C₁₃×C₁₆	—	2	2	no	—
20	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
21	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
22	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
23	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
24	C₁₃×#97	C₈	1	1	yes	characteristic
25	C₁₃×#97	C₈	1	1	yes	characteristic
26	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₁₃×C₃₂	—	2	2	no	—
29	C₁₃×C₃₂	—	2	2	no	—
30	#13641	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
32	C₁₃×M₁₆	—	2	2	no	—
33	C₂×C₈×C₁₃	—	2	1	no	—
34	C₂×C₈×C₁₃	—	2	1	no	—
35	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
36	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
37	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
38	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
39	C₁₃×C₄⋊C₄	C₁₆	1	2	yes	—
40	C₁₃×C₂²⋊C₄	C₁₆	1	2	yes	—
41	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
42	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
43	C₁₃×C₁₆	—	2	1	no	—
44	C₁₃×C₁₆	—	2	1	no	—
45	C₁₃×C₁₆	M₁₆	1	2	yes	—
46	C₁₃×C₁₆	#41	1	2	yes	—
47	#2108	C₂×C₁₃	1	1	yes	characteristic
48	C₄⋊C₃₂	C₂×C₁₃	1	2	yes	complemented
49	C₂²⋊C₃₂	C₂×C₁₃	1	2	yes	—
50	#1397	C₂×C₁₃	1	1	yes	characteristic, complemented
51	C₄×C₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
52	C₂³×C₁₃	C₂×C₁₆	1	1	yes	characteristic
53	C₂×C₄×C₁₃	—	2	1	no	—
54	C₂×C₄×C₁₃	—	2	1	no	—
55	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
56	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
57	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
58	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
59	C₈×C₁₃	—	2	1	no	—
60	C₈×C₁₃	—	2	1	no	—
61	C₈×C₁₃	M₃₂	1	2	yes	—
62	C₈×C₁₃	#117	1	1	yes	characteristic
63	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
64	C₂×M₃₂	C₄×C₁₃	1	1	yes	characteristic
65	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
66	#405	C₄×C₁₃	1	1	yes	characteristic
67	C₂×C₃₂	C₂²×C₁₃	1	2	yes	—
68	C₂×C₃₂	C₂²×C₁₃	1	2	yes	—
69	#346	C₄×C₁₃	1	1	yes	characteristic
70	#346	C₄×C₁₃	1	1	yes	characteristic
71	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
72	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
73	C₂²×C₁₃	—	2	1	no	—
74	C₂²×C₁₃	—	2	2	no	—
75	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
76	C₄×C₁₃	—	2	1	no	—
77	C₄×C₁₃	—	2	2	no	—
78	C₄×C₁₃	—	2	2	no	—
79	C₄×C₁₃	#431	1	1	yes	characteristic
80	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
81	C₂×M₁₆	C₈×C₁₃	1	1	yes	characteristic
82	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
83	#117	C₈×C₁₃	1	1	yes	characteristic
84	M₃₂	—	2	2	no	—
85	C₂×C₁₆	—	2	2	no	—
86	C₂×C₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
87	C₂×C₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
88	C₂×C₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
89	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
90	#97	C₈×C₁₃	1	1	yes	characteristic
91	#97	C₈×C₁₃	1	1	yes	characteristic
92	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
93	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
94	C₃₂	—	2	2	no	—
95	C₃₂	—	2	2	no	—
96	C₂×C₁₃	—	4	1	no	—
97	C₂×C₁₃	#2162	1	1	yes	characteristic
98	C₂×C₁₃	#2258	1	2	yes	—
99	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
100	M₁₆	—	2	2	no	—
101	C₂×C₈	—	2	1	no	—
102	C₂×C₈	—	2	1	no	—
103	C₂×C₈	C₂×C₈×C₁₃	1	1	yes	characteristic
104	C₂×C₈	C₂×C₈×C₁₃	1	1	yes	characteristic
105	C₂×C₈	C₂×C₈×C₁₃	1	1	yes	characteristic
106	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
107	C₄⋊C₄	C₁₃×C₁₆	1	2	yes	—
108	C₂²⋊C₄	C₁₃×C₁₆	1	2	yes	—
109	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
110	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
111	C₁₆	—	2	1	no	—
112	C₁₆	—	2	1	no	—
113	C₁₆	C₁₃×M₁₆	1	2	yes	—
114	C₁₆	C₁₃×#41	1	2	yes	—
115	C₁₃	#13641	1	1	yes	characteristic, direct product factor, Sylow
116	C₂³	C₂×C₁₃×C₁₆	1	1	yes	characteristic
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	2	1	no	—
119	C₂×C₄	C₂×C₁₃×C₁₆	1	2	yes	—
120	C₂×C₄	C₂×C₁₃×C₁₆	1	2	yes	—
121	C₂×C₄	C₂×C₁₃×C₁₆	1	1	yes	characteristic
122	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
123	C₈	—	2	1	no	—
124	C₈	—	2	1	no	—
125	C₈	C₁₃×M₃₂	1	2	yes	—
126	C₈	C₁₃×#117	1	1	yes	characteristic
127	C₈	C₂×C₁₃×M₁₆	1	1	yes	characteristic
128	C₂²	—	2	2	no	—
129	C₂²	—	2	1	no	—
130	C₂²	C₂²×C₁₃×C₁₆	1	1	yes	characteristic
131	C₄	—	2	2	no	—
132	C₄	—	2	2	no	—
133	C₄	—	2	1	no	—
134	C₄	C₁₃×#431	1	1	yes	characteristic
135	C₄	C₂×C₁₃×M₃₂	1	1	yes	characteristic
136	C₂	—	4	1	no	—
137	C₂	C₁₃×#2162	1	1	yes	characteristic
138	C₂	C₁₃×#2258	1	2	yes	—

	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
5. C₄×C₁₃×C₃₂	C₂	semidirect
30. #13641	C₁₃	direct (N × H)
48. C₄⋊C₃₂	C₂×C₁₃	semidirect
50. #1397	C₂×C₁₃	semidirect
51. C₄×C₃₂	C₂×C₁₃	semidirect
115. C₁₃	#13641	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2108	2
C₁₃×C₄⋊C₃₂	2
C₁₃×C₂²⋊C₃₂	2
C₁₃×#1397	2
C₄×C₁₃×C₃₂	2
#13641	13

Subgroups — C13×#13641 #15699980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13641 #15699980