Subgroups — C₁₃×#13628 #15699967

Order 3328.

206 conjugacy classes of subgroups.

The subgroup lattice has 124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×M₆₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2108	C₂	1	1	yes	maximal, characteristic
4	C₁₃×C₄⋊C₃₂	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×M₃₂	C₄	1	1	yes	characteristic
6	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₁₃×#405	C₄	1	1	yes	characteristic
8	C₁₃×M₆₄	—	2	2	no	—
9	C₂×C₁₃×C₃₂	—	2	2	no	—
10	C₂×C₁₃×C₃₂	C₂²	1	2	yes	—
11	C₂×C₁₃×C₃₂	C₂²	1	2	yes	—
12	C₁₃×#346	C₄	1	2	yes	—
13	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
14	C₂×C₁₃×M₁₆	C₈	1	1	yes	characteristic
15	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₁₃×#117	C₈	1	1	yes	characteristic
17	C₁₃×M₃₂	—	2	2	no	—
18	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
19	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
20	C₂×C₁₃×C₁₆	D₄	1	2	yes	—
21	C₂×C₁₃×C₁₆	Q₈	1	2	yes	—
22	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
23	C₁₃×#97	C₈	1	2	yes	—
24	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
25	C₁₃×C₃₂	—	2	2	no	—
26	C₁₃×C₃₂	—	2	2	no	—
27	#13628	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
29	C₁₃×M₁₆	—	2	2	no	—
30	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
31	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
32	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
33	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
34	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
35	C₁₃×C₄⋊C₄	C₁₆	1	2	yes	—
36	C₁₃×C₂²⋊C₄	C₁₆	1	2	yes	—
37	C₄²×C₁₃	C₂×C₈	1	2	yes	—
38	C₁₃×C₁₆	—	2	2	no	—
39	C₁₃×C₁₆	C₄⋊C₄	1	2	yes	—
40	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
41	C₁₃×C₁₆	C₂×Q₈	1	1	yes	characteristic
42	C₂×M₆₄	C₂×C₁₃	1	1	yes	characteristic
43	C₂²×C₃₂	C₂×C₁₃	1	1	yes	characteristic
44	#2108	C₂×C₁₃	1	1	yes	characteristic
45	C₄⋊C₃₂	C₂×C₁₃	1	4	yes	complemented
46	C₂³×C₁₃	C₂×C₁₆	1	1	yes	characteristic
47	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
48	C₂×C₄×C₁₃	C₂×C₁₆	1	4	yes	—
49	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
50	C₂×C₄×C₁₃	M₃₂	1	2	yes	—
51	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
52	C₈×C₁₃	—	2	2	no	—
53	C₈×C₁₃	C₄⋊C₈	1	2	yes	—
54	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
55	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
56	C₂×M₃₂	C₄×C₁₃	1	1	yes	characteristic
57	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
58	#405	C₄×C₁₃	1	1	yes	characteristic
59	M₆₄	—	2	2	no	—
60	C₂×C₃₂	—	2	2	no	—
61	C₂×C₃₂	C₂²×C₁₃	1	2	yes	—
62	C₂×C₃₂	C₂²×C₁₃	1	2	yes	—
63	#346	C₄×C₁₃	1	2	yes	—
64	C₄×C₁₆	C₂²×C₁₃	1	2	yes	—
65	C₂²×C₁₃	—	2	2	no	—
66	C₂²×C₁₃	C₄⋊C₁₆	1	2	yes	—
67	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
68	C₄×C₁₃	—	2	4	no	—
69	C₄×C₁₃	C₄⋊C₁₆	1	2	yes	—
70	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
71	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
72	C₂×M₁₆	C₈×C₁₃	1	1	yes	characteristic
73	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
74	#117	C₈×C₁₃	1	1	yes	characteristic
75	M₃₂	—	2	2	no	—
76	C₂×C₁₆	C₂×C₄×C₁₃	1	2	yes	—
77	C₂×C₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
78	C₂×C₁₆	D₄×C₁₃	1	2	yes	—
79	C₂×C₁₆	Q₈×C₁₃	1	2	yes	—
80	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
81	#97	C₈×C₁₃	1	2	yes	—
82	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
83	C₃₂	—	2	2	no	—
84	C₃₂	—	2	2	no	—
85	C₂×C₁₃	—	2	2	no	—
86	C₂×C₁₃	C₂×C₄⋊C₁₆	1	1	yes	characteristic
87	C₂×C₁₃	#2258	1	2	yes	—
88	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
89	M₁₆	—	2	2	no	—
90	C₂×C₈	C₁₃×C₄⋊C₄	1	2	yes	—
91	C₂×C₈	C₂×C₈×C₁₃	1	2	yes	—
92	C₂×C₈	C₂×C₈×C₁₃	1	1	yes	characteristic
93	C₂×C₈	C₁₃×M₁₆	1	2	yes	—
94	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
95	C₄⋊C₄	C₁₃×C₁₆	1	2	yes	—
96	C₂²⋊C₄	C₁₃×C₁₆	1	2	yes	—
97	C₄²	C₂×C₈×C₁₃	1	2	yes	—
98	C₁₆	—	2	2	no	—
99	C₁₆	C₁₃×C₄⋊C₄	1	2	yes	—
100	C₁₆	C₂×D₄×C₁₃	1	1	yes	characteristic
101	C₁₆	C₂×Q₈×C₁₃	1	1	yes	characteristic
102	C₁₃	#13628	1	1	yes	characteristic, direct product factor, Sylow
103	C₂³	C₂×C₁₃×C₁₆	1	1	yes	characteristic
104	C₂×C₄	C₁₃×C₄⋊C₈	1	2	yes	—
105	C₂×C₄	C₂×C₁₃×C₁₆	1	4	yes	—
106	C₂×C₄	C₂×C₁₃×C₁₆	1	1	yes	characteristic
107	C₂×C₄	C₁₃×M₃₂	1	2	yes	—
108	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
109	C₈	—	2	2	no	—
110	C₈	C₁₃×C₄⋊C₈	1	2	yes	—
111	C₈	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
112	C₈	C₂×C₁₃×M₁₆	1	1	yes	characteristic
113	C₂²	—	2	2	no	—
114	C₂²	C₁₃×C₄⋊C₁₆	1	2	yes	—
115	C₂²	C₂²×C₁₃×C₁₆	1	1	yes	characteristic
116	C₄	—	2	4	no	—
117	C₄	C₁₃×C₄⋊C₁₆	1	2	yes	—
118	C₄	C₂×C₁₃×C₄⋊C₈	1	1	yes	characteristic
119	C₄	C₂×C₁₃×M₃₂	1	1	yes	characteristic
120	C₂	—	2	2	no	—
121	C₂	C₂×C₁₃×C₄⋊C₁₆	1	1	yes	characteristic
122	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
4. C₁₃×C₄⋊C₃₂	C₂	semidirect
27. #13628	C₁₃	direct (N × H)
45. C₄⋊C₃₂	C₂×C₁₃	semidirect
102. C₁₃	#13628	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×C₁₃×M₆₄	2
C₂²×C₁₃×C₃₂	2
C₁₃×#2108	2
C₁₃×C₄⋊C₃₂	2
#13628	13

Subgroups — C13×#13628 #15699967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13628 #15699967