Subgroups — C₁₃×#8268 #15694607

Order 3328.

390 conjugacy classes of subgroups.

The subgroup lattice has 152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1564	C₂	1	2	yes	maximal
3	C₁₃×#1450	C₂	1	2	yes	maximal
4	C₁₃×#1276	C₂	1	2	yes	maximal
5	C₁₃×#431	C₂²	1	4	yes	—
6	C₂×C₁₃×#97	C₄	1	2	yes	—
7	C₂×C₁₃×#97	C₄	1	2	yes	—
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₄³×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×#335	C₄	1	4	yes	complemented
12	C₁₃×#334	C₄	1	4	yes	complemented
13	C₁₃×#322	—	2	2	no	—
14	C₈²×C₁₃	—	2	2	no	—
15	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₁₃	—	2	2	no	—
19	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
21	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
22	C₁₃×C₂²⋊C₈	—	2	4	no	—
23	C₁₃×#97	—	2	4	no	—
24	C₁₃×#97	C₈	1	8	yes	complemented
25	C₄×C₈×C₁₃	—	2	4	no	—
26	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
27	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
28	C₄×C₈×C₁₃	D₄	1	2	yes	—
29	C₄×C₈×C₁₃	Q₈	1	2	yes	—
30	#8268	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂²×C₄×C₁₃	—	2	2	no	—
32	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₃	#41	1	2	yes	—
34	C₂×C₈×C₁₃	—	2	2	no	—
35	C₂×C₈×C₁₃	—	2	8	no	—
36	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
37	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
38	C₂×C₈×C₁₃	C₄²	1	2	yes	—
39	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
40	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
41	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
42	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
43	C₄²×C₁₃	—	2	2	no	—
44	C₄²×C₁₃	—	4	4	no	—
45	C₄²×C₁₃	C₂×C₈	1	4	yes	—
46	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
47	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
48	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
49	C₄×#97	C₂×C₁₃	1	1	yes	characteristic
50	#1564	C₂×C₁₃	1	2	yes	—
51	#1450	C₂×C₁₃	1	2	yes	—
52	#1276	C₂×C₁₃	1	2	yes	—
53	C₂³×C₁₃	#117	1	1	yes	characteristic
54	C₂×C₄×C₁₃	—	2	4	no	—
55	C₂×C₄×C₁₃	—	2	4	no	—
56	C₂×C₄×C₁₃	—	4	4	no	—
57	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
58	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
60	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
61	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
62	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
63	C₈×C₁₃	—	2	1	no	—
64	C₈×C₁₃	—	2	1	no	—
65	C₈×C₁₃	—	4	8	no	—
66	C₈×C₁₃	C₄×C₈	1	4	yes	—
67	C₈×C₁₃	C₄⋊C₈	1	8	yes	—
68	#431	C₂²×C₁₃	1	4	yes	—
69	C₂×#97	C₄×C₁₃	1	2	yes	—
70	C₂×#97	C₄×C₁₃	1	2	yes	—
71	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
72	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
73	C₄³	C₂²×C₁₃	1	1	yes	characteristic
74	#335	C₄×C₁₃	1	4	yes	complemented
75	#334	C₄×C₁₃	1	4	yes	complemented
76	#322	—	2	2	no	—
77	C₈²	—	2	2	no	—
78	C₂²×C₁₃	—	2	2	no	—
79	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₁₃	#431	1	2	yes	—
81	C₄×C₁₃	—	2	2	no	—
82	C₄×C₁₃	—	4	4	no	—
83	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
84	C₄×C₁₃	C₄×M₁₆	1	1	yes	characteristic
85	C₄×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
86	C₄×C₁₃	#444	1	4	yes	—
87	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
88	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
89	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
90	C₂×C₄²	—	2	2	no	—
91	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
92	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
93	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
94	C₂²⋊C₈	—	2	4	no	—
95	#97	—	2	4	no	—
96	#97	C₈×C₁₃	1	8	yes	complemented
97	C₄×C₈	—	2	4	no	—
98	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
99	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
100	C₄×C₈	D₄×C₁₃	1	2	yes	—
101	C₄×C₈	Q₈×C₁₃	1	2	yes	—
102	C₂×C₁₃	—	2	2	no	—
103	C₂×C₁₃	C₄×C₄⋊C₈	1	1	yes	characteristic
104	C₂×C₁₃	#1773	1	2	yes	—
105	C₂²×C₄	—	2	2	no	—
106	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
107	C₂²×C₄	C₁₃×#41	1	2	yes	—
108	C₂×C₈	—	2	2	no	—
109	C₂×C₈	—	2	8	no	—
110	C₂×C₈	C₄²×C₁₃	1	1	yes	characteristic
111	C₂×C₈	C₄²×C₁₃	1	1	yes	characteristic
112	C₂×C₈	C₄²×C₁₃	1	2	yes	—
113	C₂×C₈	C₁₃×C₄⋊C₄	1	4	yes	—
114	C₂×C₈	C₂×C₈×C₁₃	1	4	yes	—
115	C₂×C₈	C₂×C₈×C₁₃	1	4	yes	—
116	C₂×C₈	C₁₃×M₁₆	1	4	yes	—
117	C₄²	—	2	2	no	—
118	C₄²	—	4	4	no	—
119	C₄²	C₂×C₈×C₁₃	1	4	yes	—
120	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
121	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
122	C₄²	C₂×Q₈×C₁₃	1	1	yes	characteristic
123	C₁₃	#8268	1	1	yes	characteristic, direct product factor, Sylow
124	C₂³	C₁₃×#117	1	1	yes	characteristic
125	C₂×C₄	—	2	4	no	—
126	C₂×C₄	—	2	4	no	—
127	C₂×C₄	—	4	4	no	—
128	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
129	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
131	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
132	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
133	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
134	C₈	—	2	1	no	—
135	C₈	—	2	1	no	—
136	C₈	—	4	8	no	—
137	C₈	C₄×C₈×C₁₃	1	4	yes	—
138	C₈	C₁₃×C₄⋊C₈	1	8	yes	—
139	C₂²	—	2	2	no	—
140	C₂²	C₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
141	C₂²	C₁₃×#431	1	2	yes	—
142	C₄	—	2	2	no	—
143	C₄	—	4	4	no	—
144	C₄	C₂×C₄×C₈×C₁₃	1	1	yes	characteristic
145	C₄	C₄×C₁₃×M₁₆	1	1	yes	characteristic
146	C₄	C₂×C₁₃×C₄⋊C₈	1	2	yes	—
147	C₄	C₁₃×#444	1	4	yes	—
148	C₂	—	2	2	no	—
149	C₂	C₄×C₁₃×C₄⋊C₈	1	1	yes	characteristic
150	C₂	C₁₃×#1773	1	2	yes	—

	subgroup	G/H
center	C₄²×C₁₃	C₂×D₄
commutator	C₄	C₂×C₄×C₈×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle	C₂²×C₁₃	C₄×C₄⋊C₄
prime radical	C₂³×C₁₃	#117
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
11. C₁₃×#335	C₄	semidirect
12. C₁₃×#334	C₄	semidirect
24. C₁₃×#97	C₈	semidirect
30. #8268	C₁₃	direct (N × H)
74. #335	C₄×C₁₃	semidirect
75. #334	C₄×C₁₃	semidirect
96. #97	C₈×C₁₃	semidirect
123. C₁₃	#8268	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₃×#97	2
C₁₃×#1564	2
C₁₃×#1450	2
C₁₃×#1276	2
#8268	13

Subgroups — C13×#8268 #15694607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#8268 #15694607