Subgroups — C₁₃×#12594 #15698933

Order 3328.

354 conjugacy classes of subgroups.

The subgroup lattice has 136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×M₃₂	C₂	1	2	yes	maximal
2	C₄×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1375	C₂	1	4	yes	maximal
4	C₂×C₁₃×M₃₂	C₂²	1	4	yes	—
5	C₂×C₁₃×#97	C₄	1	2	yes	—
6	C₂×C₁₃×#97	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₄³×C₁₃	C₄	1	1	yes	characteristic
10	C₁₃×#346	C₄	1	4	yes	complemented
11	C₄×C₁₃×C₁₆	C₄	1	4	yes	complemented
12	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
13	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
15	C₂×C₄²×C₁₃	—	2	2	no	—
16	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₁₃×M₃₂	—	2	8	no	—
19	C₂×C₁₃×C₁₆	C₂×C₄	1	8	yes	—
20	C₁₃×#97	—	2	4	no	—
21	C₁₃×#97	C₈	1	8	yes	—
22	C₄×C₈×C₁₃	—	2	2	no	—
23	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
24	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
25	#12594	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	C₂²×C₄×C₁₃	—	2	2	no	—
27	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
28	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₈×C₁₃	—	2	2	no	—
30	C₂×C₈×C₁₃	—	2	2	no	—
31	C₂×C₈×C₁₃	C₄²	1	2	yes	—
32	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
33	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
34	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
35	C₂×C₈×C₁₃	#41	1	4	yes	—
36	C₄²×C₁₃	—	2	2	no	—
37	C₄²×C₁₃	—	4	4	no	—
38	C₄²×C₁₃	C₄²	1	1	yes	characteristic
39	C₄²×C₁₃	C₄²	1	1	yes	characteristic
40	C₄²×C₁₃	C₂×C₈	1	4	yes	—
41	C₄²×C₁₃	M₁₆	1	2	yes	—
42	C₁₃×C₁₆	—	2	8	no	—
43	C₄×M₃₂	C₂×C₁₃	1	2	yes	—
44	C₄×#97	C₂×C₁₃	1	1	yes	characteristic
45	#1375	C₂×C₁₃	1	4	yes	—
46	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
47	C₂×C₄×C₁₃	—	2	4	no	—
48	C₂×C₄×C₁₃	—	2	4	no	—
49	C₂×C₄×C₁₃	—	4	4	no	—
50	C₂×C₄×C₁₃	#97	1	2	yes	—
51	C₂×C₄×C₁₃	#97	1	2	yes	—
52	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
53	C₂×C₄×C₁₃	#117	1	2	yes	—
54	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
55	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
56	C₈×C₁₃	—	2	4	no	—
57	C₈×C₁₃	C₄×C₈	1	4	yes	—
58	C₈×C₁₃	#117	1	4	yes	—
59	C₂×M₃₂	C₂²×C₁₃	1	4	yes	—
60	C₂×#97	C₄×C₁₃	1	2	yes	—
61	C₂×#97	C₂²×C₁₃	1	2	yes	—
62	C₂×C₄×C₈	C₄×C₁₃	1	1	yes	characteristic
63	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
64	C₄³	C₄×C₁₃	1	1	yes	characteristic
65	#346	C₄×C₁₃	1	4	yes	complemented
66	C₄×C₁₆	C₄×C₁₃	1	4	yes	complemented
67	C₂²×C₁₃	—	2	2	no	—
68	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
69	C₂²×C₁₃	#431	1	2	yes	—
70	C₄×C₁₃	—	2	2	no	—
71	C₄×C₁₃	—	4	4	no	—
72	C₄×C₁₃	#347	1	4	yes	—
73	C₄×C₁₃	#376	1	1	yes	characteristic
74	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
75	C₄×C₁₃	#431	1	2	yes	—
76	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
77	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
78	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
79	C₂×C₄²	—	2	2	no	—
80	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
81	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
82	M₃₂	—	2	8	no	—
83	C₂×C₁₆	C₂×C₄×C₁₃	1	8	yes	—
84	#97	—	2	4	no	—
85	#97	C₈×C₁₃	1	8	yes	—
86	C₄×C₈	—	2	2	no	—
87	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
88	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
89	C₂×C₁₃	—	2	2	no	—
90	C₂×C₁₃	#1744	1	1	yes	characteristic
91	C₂×C₁₃	C₂×#347	1	2	yes	—
92	C₂²×C₄	—	2	2	no	—
93	C₂²×C₄	C₁₃×M₁₆	1	2	yes	—
94	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
95	C₂×C₈	—	2	2	no	—
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	C₄²×C₁₃	1	2	yes	—
98	C₂×C₈	C₂×C₈×C₁₃	1	4	yes	—
99	C₂×C₈	C₂×C₈×C₁₃	1	4	yes	—
100	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
101	C₂×C₈	C₁₃×#41	1	4	yes	—
102	C₄²	—	2	2	no	—
103	C₄²	—	4	4	no	—
104	C₄²	C₄²×C₁₃	1	1	yes	characteristic
105	C₄²	C₄²×C₁₃	1	1	yes	characteristic
106	C₄²	C₂×C₈×C₁₃	1	4	yes	—
107	C₄²	C₁₃×M₁₆	1	2	yes	—
108	C₁₆	—	2	8	no	—
109	C₁₃	#12594	1	1	yes	characteristic, direct product factor, Sylow
110	C₂³	C₂×C₁₃×M₁₆	1	1	yes	characteristic
111	C₂×C₄	—	2	4	no	—
112	C₂×C₄	—	2	4	no	—
113	C₂×C₄	—	4	4	no	—
114	C₂×C₄	C₁₃×#97	1	2	yes	—
115	C₂×C₄	C₁₃×#97	1	2	yes	—
116	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
117	C₂×C₄	C₁₃×#117	1	2	yes	—
118	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
119	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
120	C₈	—	2	4	no	—
121	C₈	C₄×C₈×C₁₃	1	4	yes	—
122	C₈	C₁₃×#117	1	4	yes	—
123	C₂²	—	2	2	no	—
124	C₂²	C₂×C₁₃×#97	1	1	yes	characteristic
125	C₂²	C₁₃×#431	1	2	yes	—
126	C₄	—	2	2	no	—
127	C₄	—	4	4	no	—
128	C₄	C₁₃×#347	1	4	yes	—
129	C₄	C₁₃×#376	1	1	yes	characteristic
130	C₄	C₂×C₄×C₈×C₁₃	1	1	yes	characteristic
131	C₄	C₁₃×#431	1	2	yes	—
132	C₂	—	2	2	no	—
133	C₂	C₁₃×#1744	1	1	yes	characteristic
134	C₂	C₂×C₁₃×#347	1	2	yes	—

	subgroup	G/H
center	C₄²×C₁₃	C₄²
commutator	C₄	C₂×C₄×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×#97
prime radical	C₂³×C₁₃	C₂×M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
10. C₁₃×#346	C₄	semidirect
11. C₄×C₁₃×C₁₆	C₄	semidirect
25. #12594	C₁₃	direct (N × H)
65. #346	C₄×C₁₃	semidirect
66. C₄×C₁₆	C₄×C₁₃	semidirect
109. C₁₃	#12594	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×M₃₂	2
C₄×C₁₃×#97	2
C₁₃×#1375	2
#12594	13

Subgroups — C13×#12594 #15698933

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12594 #15698933