Subgroups — C₁₃×#12901 #15699240

Order 3328.

342 conjugacy classes of subgroups.

The subgroup lattice has 138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#364	C₂	1	4	yes	maximal
2	C₁₃×#2150	C₂	1	2	yes	maximal
3	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×M₃₂	C₂²	1	4	yes	—
5	C₂×C₁₃×#97	C₄	1	2	yes	—
6	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#376	C₄	1	1	yes	characteristic
10	C₁₃×#364	—	2	8	no	—
11	C₁₃×C₄⋊C₁₆	—	2	4	no	—
12	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
14	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
15	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₁₃×M₃₂	—	2	8	no	—
18	C₂×C₁₃×C₁₆	—	2	4	no	—
19	C₁₃×#97	—	2	4	no	—
20	C₁₃×#97	C₈	1	4	yes	—
21	C₄×C₈×C₁₃	D₄	1	4	yes	—
22	C₄×C₈×C₁₃	D₄	1	2	yes	—
23	C₄×C₈×C₁₃	Q₈	1	4	yes	—
24	C₄×C₈×C₁₃	Q₈	1	2	yes	—
25	C₁₃×#95	—	2	2	no	—
26	#12901	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂²×C₄×C₁₃	—	2	2	no	—
28	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
29	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₈×C₁₃	—	2	2	no	—
31	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
32	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
33	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
34	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
35	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
36	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
37	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
39	C₄²×C₁₃	—	2	2	no	—
40	C₄²×C₁₃	C₄⋊C₄	1	4	yes	—
41	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
42	C₄²×C₁₃	C₂×C₈	1	2	yes	—
43	C₁₃×C₁₆	—	4	4	no	—
44	C₂×#364	C₂×C₁₃	1	4	yes	—
45	#2150	C₂×C₁₃	1	2	yes	—
46	#1726	C₂×C₁₃	1	1	yes	characteristic
47	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
48	C₂×C₄×C₁₃	—	2	4	no	—
49	C₂×C₄×C₁₃	—	4	2	no	—
50	C₂×C₄×C₁₃	—	4	4	no	—
51	C₂×C₄×C₁₃	C₄⋊C₈	1	4	yes	—
52	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
53	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
55	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
56	C₈×C₁₃	—	2	2	no	—
57	C₈×C₁₃	C₄⋊C₈	1	8	yes	—
58	C₈×C₁₃	#127	1	1	yes	characteristic
59	C₈×C₁₃	C₄⋊Q₈	1	2	yes	—
60	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
61	C₂×M₃₂	C₂²×C₁₃	1	4	yes	—
62	C₂×#97	C₄×C₁₃	1	2	yes	—
63	C₂×#97	C₄×C₁₃	1	1	yes	characteristic
64	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
65	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
66	#376	C₄×C₁₃	1	1	yes	characteristic
67	#364	—	2	8	no	—
68	C₄⋊C₁₆	—	2	4	no	—
69	C₂²×C₁₃	—	2	2	no	—
70	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
71	C₂²×C₁₃	#423	1	2	yes	—
72	C₄×C₁₃	—	2	4	no	—
73	C₄×C₁₃	—	4	4	no	—
74	C₄×C₁₃	#384	1	1	yes	characteristic
75	C₄×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
76	C₄×C₁₃	#423	1	1	yes	characteristic
77	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
78	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
79	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
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	—	2	4	no	—
84	#97	—	2	4	no	—
85	#97	C₈×C₁₃	1	4	yes	—
86	C₄×C₈	D₄×C₁₃	1	2	yes	—
87	C₄×C₈	D₄×C₁₃	1	4	yes	—
88	C₄×C₈	Q₈×C₁₃	1	4	yes	—
89	C₄×C₈	Q₈×C₁₃	1	2	yes	—
90	#95	—	2	2	no	—
91	C₂×C₁₃	—	2	2	no	—
92	C₂×C₁₃	#1842	1	1	yes	characteristic
93	C₂×C₁₃	#2153	1	2	yes	—
94	C₂²×C₄	—	2	2	no	—
95	C₂²×C₄	C₁₃×M₁₆	1	2	yes	—
96	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
97	C₂×C₈	—	2	2	no	—
98	C₂×C₈	C₁₃×C₄⋊C₄	1	2	yes	—
99	C₂×C₈	C₁₃×C₄⋊C₄	1	4	yes	—
100	C₂×C₈	C₂×C₈×C₁₃	1	4	yes	—
101	C₂×C₈	C₁₃×M₁₆	1	4	yes	—
102	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
103	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
104	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
105	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
106	C₄²	—	2	2	no	—
107	C₄²	C₁₃×C₄⋊C₄	1	4	yes	—
108	C₄²	C₁₃×C₄⋊C₄	1	2	yes	—
109	C₄²	C₂×C₈×C₁₃	1	2	yes	—
110	C₁₆	—	4	4	no	—
111	C₁₃	#12901	1	1	yes	characteristic, direct product factor, Sylow
112	C₂³	C₂×C₁₃×M₁₆	1	1	yes	characteristic
113	C₂×C₄	—	2	4	no	—
114	C₂×C₄	—	4	2	no	—
115	C₂×C₄	—	4	4	no	—
116	C₂×C₄	C₁₃×C₄⋊C₈	1	4	yes	—
117	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
118	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
120	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
121	C₈	—	2	2	no	—
122	C₈	C₁₃×C₄⋊C₈	1	8	yes	—
123	C₈	C₁₃×#127	1	1	yes	characteristic
124	C₈	C₁₃×C₄⋊Q₈	1	2	yes	—
125	C₈	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
126	C₂²	—	2	2	no	—
127	C₂²	C₂×C₁₃×C₄⋊C₈	1	1	yes	characteristic
128	C₂²	C₁₃×#423	1	2	yes	—
129	C₄	—	2	4	no	—
130	C₄	—	4	4	no	—
131	C₄	C₁₃×#384	1	1	yes	characteristic
132	C₄	C₂×C₁₃×C₄⋊C₈	1	2	yes	—
133	C₄	C₁₃×#423	1	1	yes	characteristic
134	C₂	—	2	2	no	—
135	C₂	C₁₃×#1842	1	1	yes	characteristic
136	C₂	C₁₃×#2153	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₁₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×C₄⋊C₈
prime radical	C₂³×C₁₃	C₂×M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
26. #12901	C₁₃	direct (N × H)
111. C₁₃	#12901	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×#364	2
C₁₃×#2150	2
C₁₃×#1726	2
#12901	13

Subgroups — C13×#12901 #15699240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12901 #15699240