Subgroups — C₂×C₁₃×#2253 #15720063

Order 3328.

494 conjugacy classes of subgroups.

The subgroup lattice has 148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#499	C₂	1	2	yes	maximal
2	C₁₃×#2253	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₁₃×#367	C₂	1	2	yes	maximal
4	C₂×C₁₃×#366	C₂	1	2	yes	maximal
5	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#125	—	2	2	no	—
7	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
9	C₁₃×#499	—	2	4	no	—
10	C₁₃×#499	C₂²	1	8	yes	—
11	C₂×C₁₃×#107	C₂²	1	4	yes	—
12	C₂×C₁₃×#106	—	2	2	no	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#367	C₂²	1	8	yes	—
15	C₁₃×#366	C₂²	1	8	yes	—
16	C₄×C₁₃×C₁₆	C₂²	1	4	yes	—
17	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
19	C₁₃×#125	—	2	8	no	—
20	C₁₃×#125	—	4	4	no	—
21	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
22	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
23	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
24	C₂×C₁₃×C₁₆	Q₈	1	4	yes	—
25	C₂×C₁₃×C₁₆	Q₈	1	4	yes	—
26	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
27	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
28	C₁₃×#107	—	2	4	no	—
29	C₁₃×#107	C₂³	1	8	yes	—
30	C₁₃×#106	—	2	8	no	—
31	C₄×C₈×C₁₃	D₄	1	2	yes	—
32	C₄×C₈×C₁₃	C₂³	1	2	yes	—
33	C₂×#2253	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₂²×C₄×C₁₃	—	4	4	no	—
35	C₂²×C₄×C₁₃	D₈	1	2	yes	—
36	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
37	C₂×C₈×C₁₃	Q₁₆	1	4	yes	—
38	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
40	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
41	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
42	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
43	C₁₃×C₄⋊C₄	—	2	8	no	—
44	C₁₃×C₄⋊C₄	—	4	4	no	—
45	C₁₃×C₄⋊C₄	—	4	16	no	—
46	C₄²×C₁₃	D₈	1	2	yes	—
47	C₄²×C₁₃	C₂×D₄	1	2	yes	—
48	C₁₃×C₁₆	C₂×Q₈	1	4	yes	—
49	C₁₃×C₁₆	C₂×Q₈	1	4	yes	—
50	C₂×#499	C₂×C₁₃	1	2	yes	—
51	#2253	C₂×C₁₃	1	8	yes	direct product factor
52	C₂×#367	C₂×C₁₃	1	2	yes	—
53	C₂×#366	C₂×C₁₃	1	2	yes	—
54	C₂×C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic
55	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
56	C₂×C₄×C₁₃	—	2	4	no	—
57	C₂×C₄×C₁₃	—	4	8	no	—
58	C₂×C₄×C₁₃	—	8	8	no	—
59	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
60	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
61	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
62	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
63	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
64	C₈×C₁₃	C₄⋊Q₈	1	2	yes	—
65	C₈×C₁₃	C₂×Q₁₆	1	4	yes	—
66	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
67	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
68	C₂×#125	—	2	2	no	—
69	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
70	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
71	#499	—	2	4	no	—
72	#499	C₂²×C₁₃	1	8	yes	—
73	C₂×#107	C₂²×C₁₃	1	4	yes	—
74	C₂×#106	—	2	2	no	—
75	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
76	#367	C₂²×C₁₃	1	8	yes	—
77	#366	C₂²×C₁₃	1	8	yes	—
78	C₄×C₁₆	C₂²×C₁₃	1	4	yes	—
79	C₂²×C₁₃	#500	1	2	yes	—
80	C₂²×C₁₃	#508	1	4	yes	—
81	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
82	C₄×C₁₃	—	2	4	no	—
83	C₄×C₁₃	—	8	8	no	—
84	C₄×C₁₃	#500	1	2	yes	—
85	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
86	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
87	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
88	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
89	#125	—	2	8	no	—
90	#125	—	4	4	no	—
91	C₂×C₄⋊C₄	—	2	4	no	—
92	C₂×C₄⋊C₄	—	4	4	no	—
93	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
94	C₂×C₁₆	Q₈×C₁₃	1	4	yes	—
95	C₂×C₁₆	Q₈×C₁₃	1	4	yes	—
96	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
97	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
98	#107	—	2	4	no	—
99	#107	C₂³×C₁₃	1	8	yes	—
100	#106	—	2	8	no	—
101	C₄×C₈	D₄×C₁₃	1	2	yes	—
102	C₄×C₈	C₂³×C₁₃	1	2	yes	—
103	C₂×C₁₃	#2253	1	4	yes	direct product factor
104	C₂×C₁₃	C₂×#500	1	1	yes	characteristic
105	C₂×C₁₃	C₂×#508	1	2	yes	—
106	C₂²×C₄	—	4	4	no	—
107	C₂²×C₄	C₁₃×D₈	1	2	yes	—
108	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
109	C₂×C₈	C₁₃×Q₁₆	1	4	yes	—
110	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
111	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
112	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
113	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
114	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
115	C₄⋊C₄	—	2	8	no	—
116	C₄⋊C₄	—	4	4	no	—
117	C₄⋊C₄	—	4	16	no	—
118	C₄²	C₁₃×D₈	1	2	yes	—
119	C₄²	C₂×D₄×C₁₃	1	2	yes	—
120	C₁₆	C₂×Q₈×C₁₃	1	4	yes	—
121	C₁₆	C₂×Q₈×C₁₃	1	4	yes	—
122	C₁₃	C₂×#2253	1	1	yes	characteristic, direct product factor, Sylow
123	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
124	C₂×C₄	—	2	4	no	—
125	C₂×C₄	—	4	8	no	—
126	C₂×C₄	—	8	8	no	—
127	C₂×C₄	C₁₃×C₄⋊Q₈	1	2	yes	—
128	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
129	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
130	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
131	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
132	C₈	C₁₃×C₄⋊Q₈	1	2	yes	—
133	C₈	C₂×C₁₃×Q₁₆	1	4	yes	—
134	C₈	C₂²×Q₈×C₁₃	1	1	yes	characteristic
135	C₈	C₂²×Q₈×C₁₃	1	1	yes	characteristic
136	C₂²	C₁₃×#500	1	2	yes	—
137	C₂²	C₁₃×#508	1	4	yes	—
138	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
139	C₄	—	2	4	no	—
140	C₄	—	8	8	no	—
141	C₄	C₁₃×#500	1	2	yes	—
142	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
143	C₄	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
144	C₂	C₁₃×#2253	1	4	yes	direct product factor
145	C₂	C₂×C₁₃×#500	1	1	yes	characteristic
146	C₂	C₂×C₁₃×#508	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2253	C₂	direct (N × H)
33. C₂×#2253	C₁₃	direct (N × H)
51. #2253	C₂×C₁₃	direct (N × H)
103. C₂×C₁₃	#2253	direct (N × H)
122. C₁₃	C₂×#2253	direct (N × H)
144. C₂	C₁₃×#2253	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×#499	2
C₁₃×#2253	2
C₂×C₁₃×#367	2
C₂×C₁₃×#366	2
C₂×C₄×C₁₃×C₁₆	2
C₂×#2253	13

Subgroups — C2×C13×#2253 #15720063

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2253 #15720063