Subgroups — C₁₃×#7844 #15694183

Order 3328.

518 conjugacy classes of subgroups.

The subgroup lattice has 144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#1744	C₂	1	2	yes	maximal
2	C₄×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#322	C₂	1	2	yes	maximal
4	C₂×C₁₃×#322	C₂	1	1	yes	maximal, characteristic
5	C₂×C₈²×C₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#97	C₄	1	4	yes	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
9	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₄³×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#336	C₄	1	8	yes	—
13	C₁₃×#322	C₄	1	8	yes	complemented
14	C₁₃×#322	C₄	1	4	yes	complemented
15	C₈²×C₁₃	C₄	1	4	yes	complemented
16	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
17	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
18	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
19	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
21	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
22	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
23	C₁₃×#97	—	2	8	no	—
24	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
25	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
26	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
27	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
28	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
29	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
30	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
31	#7844	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
33	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
35	C₂×C₈×C₁₃	—	2	4	no	—
36	C₂×C₈×C₁₃	—	2	8	no	—
37	C₂×C₈×C₁₃	—	2	8	no	—
38	C₂×C₈×C₁₃	C₄²	1	4	yes	—
39	C₂×C₈×C₁₃	C₄²	1	8	yes	—
40	C₂×C₈×C₁₃	C₄²	1	8	yes	—
41	C₂×C₈×C₁₃	C₄²	1	4	yes	—
42	C₂×C₈×C₁₃	M₁₆	1	8	yes	—
43	C₄²×C₁₃	—	2	4	no	—
44	C₄²×C₁₃	—	2	8	no	—
45	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
46	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
47	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
48	#1744	C₂×C₁₃	1	2	yes	—
49	C₄×#97	C₂×C₁₃	1	1	yes	characteristic
50	C₂×#322	C₂×C₁₃	1	1	yes	characteristic
51	C₂×#322	C₂×C₁₃	1	2	yes	—
52	C₂×C₈²	C₂×C₁₃	1	1	yes	characteristic
53	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
54	C₂×C₄×C₁₃	—	2	4	no	—
55	C₂×C₄×C₁₃	—	2	8	no	—
56	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
57	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
58	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
59	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
60	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
61	C₂×C₄×C₁₃	#131	1	8	yes	—
62	C₈×C₁₃	—	2	4	no	—
63	C₈×C₁₃	—	2	8	no	—
64	C₈×C₁₃	—	2	8	no	—
65	C₈×C₁₃	#97	1	8	yes	—
66	C₂×#97	C₄×C₁₃	1	4	yes	—
67	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
68	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
69	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
70	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
71	C₄³	C₂²×C₁₃	1	1	yes	characteristic
72	#336	C₄×C₁₃	1	8	yes	—
73	#322	C₄×C₁₃	1	8	yes	complemented
74	#322	C₄×C₁₃	1	4	yes	complemented
75	C₈²	C₄×C₁₃	1	4	yes	complemented
76	C₂²×C₁₃	C₄³	1	1	yes	characteristic
77	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
78	C₂²×C₁₃	#405	1	4	yes	—
79	C₄×C₁₃	—	4	4	no	—
80	C₄×C₁₃	C₂×#97	1	2	yes	—
81	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
82	C₄×C₁₃	#405	1	4	yes	—
83	C₄×C₁₃	#405	1	4	yes	—
84	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
85	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
86	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
87	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
88	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
89	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
90	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
91	#97	—	2	8	no	—
92	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
93	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
94	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
95	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
96	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
97	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
98	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
99	C₂×C₁₃	#1453	1	4	yes	—
100	C₂×C₁₃	C₄×#97	1	1	yes	characteristic
101	C₂×C₁₃	#1726	1	2	yes	—
102	C₂²×C₄	C₄²×C₁₃	1	4	yes	—
103	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
104	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
105	C₂×C₈	—	2	4	no	—
106	C₂×C₈	—	2	8	no	—
107	C₂×C₈	—	2	8	no	—
108	C₂×C₈	C₄²×C₁₃	1	4	yes	—
109	C₂×C₈	C₄²×C₁₃	1	8	yes	—
110	C₂×C₈	C₄²×C₁₃	1	8	yes	—
111	C₂×C₈	C₄²×C₁₃	1	4	yes	—
112	C₂×C₈	C₁₃×M₁₆	1	8	yes	—
113	C₄²	—	2	4	no	—
114	C₄²	—	2	8	no	—
115	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
116	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
117	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
118	C₁₃	#7844	1	1	yes	characteristic, direct product factor, Sylow
119	C₂³	C₂×C₄²×C₁₃	1	1	yes	characteristic
120	C₂×C₄	—	2	4	no	—
121	C₂×C₄	—	2	8	no	—
122	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
123	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
124	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
125	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
126	C₂×C₄	C₂×C₁₃×M₁₆	1	4	yes	—
127	C₂×C₄	C₁₃×#131	1	8	yes	—
128	C₈	—	2	4	no	—
129	C₈	—	2	8	no	—
130	C₈	—	2	8	no	—
131	C₈	C₁₃×#97	1	8	yes	—
132	C₂²	C₄³×C₁₃	1	1	yes	characteristic
133	C₂²	C₄×C₁₃×M₁₆	1	2	yes	—
134	C₂²	C₁₃×#405	1	4	yes	—
135	C₄	—	4	4	no	—
136	C₄	C₂×C₁₃×#97	1	2	yes	—
137	C₄	C₄×C₁₃×M₁₆	1	2	yes	—
138	C₄	C₁₃×#405	1	4	yes	—
139	C₄	C₁₃×#405	1	4	yes	—
140	C₂	C₁₃×#1453	1	4	yes	—
141	C₂	C₄×C₁₃×#97	1	1	yes	characteristic
142	C₂	C₁₃×#1726	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²×C₁₃	C₂³
commutator	C₂²	C₄³×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle, prime radical	C₂³×C₁₃	C₂×C₄²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₁₃×#322	C₄	semidirect
14. C₁₃×#322	C₄	semidirect
15. C₈²×C₁₃	C₄	semidirect
31. #7844	C₁₃	direct (N × H)
73. #322	C₄×C₁₃	semidirect
74. #322	C₄×C₁₃	semidirect
75. C₈²	C₄×C₁₃	semidirect
118. C₁₃	#7844	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×#1744	2
C₄×C₁₃×#97	2
C₂×C₁₃×#322	2
C₂×C₈²×C₁₃	2
#7844	13

Subgroups — C13×#7844 #15694183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#7844 #15694183