Subgroups — C₂×C₁₃×#2254 #15720064

Order 3328.

558 conjugacy classes of subgroups.

The subgroup lattice has 140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#500	C₂	1	2	yes	maximal
2	C₁₃×#2254	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₁₃×#367	C₂	1	4	yes	maximal
4	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
6	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
7	C₁₃×#500	—	2	4	no	—
8	C₁₃×#500	C₂²	1	8	yes	—
9	C₂×C₁₃×#107	—	2	2	no	—
10	C₂×C₁₃×#107	C₂²	1	4	yes	—
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#367	C₂²	1	16	yes	—
13	C₄×C₁₃×C₁₆	C₂²	1	4	yes	—
14	C₂²×Q₈×C₁₃	—	4	2	no	—
15	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
17	C₁₃×C₄⋊Q₈	—	2	8	no	—
18	C₁₃×C₄⋊Q₈	—	4	4	no	—
19	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
20	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
21	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
22	C₂×C₁₃×C₁₆	Q₈	1	8	yes	complemented
23	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
24	C₁₃×#107	—	2	8	no	—
25	C₁₃×#107	—	2	4	no	—
26	C₁₃×#107	C₂³	1	8	yes	—
27	C₄×C₈×C₁₃	D₄	1	2	yes	—
28	C₄×C₈×C₁₃	C₂³	1	2	yes	—
29	C₂×#2254	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₂×Q₈×C₁₃	—	4	8	no	—
31	C₂×Q₈×C₁₃	—	8	8	no	—
32	C₂²×C₄×C₁₃	—	4	4	no	—
33	C₂²×C₄×C₁₃	D₈	1	2	yes	—
34	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₈×C₁₃	Q₁₆	1	4	yes	—
36	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
37	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
38	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
39	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
40	C₁₃×C₄⋊C₄	—	2	8	no	—
41	C₁₃×C₄⋊C₄	—	4	4	no	—
42	C₁₃×C₄⋊C₄	—	4	8	no	—
43	C₄²×C₁₃	D₈	1	2	yes	—
44	C₄²×C₁₃	C₂×D₄	1	2	yes	—
45	C₁₃×C₁₆	C₂×Q₈	1	8	yes	complemented
46	C₂×#500	C₂×C₁₃	1	2	yes	—
47	#2254	C₂×C₁₃	1	8	yes	direct product factor
48	C₂×#367	C₂×C₁₃	1	4	yes	—
49	C₂×C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic
50	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
51	Q₈×C₁₃	—	8	16	no	—
52	C₂×C₄×C₁₃	—	4	8	no	—
53	C₂×C₄×C₁₃	—	8	8	no	—
54	C₂×C₄×C₁₃	SD₃₂	1	8	yes	—
55	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
56	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
57	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
58	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
59	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
60	C₈×C₁₃	C₄⋊Q₈	1	2	yes	—
61	C₈×C₁₃	C₂×Q₁₆	1	4	yes	—
62	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
63	C₂×C₄⋊Q₈	—	2	2	no	—
64	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
65	#500	—	2	4	no	—
66	#500	C₂²×C₁₃	1	8	yes	—
67	C₂×#107	—	2	2	no	—
68	C₂×#107	C₂²×C₁₃	1	4	yes	—
69	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
70	#367	C₂²×C₁₃	1	16	yes	—
71	C₄×C₁₆	C₂²×C₁₃	1	4	yes	—
72	C₂²×C₁₃	#500	1	2	yes	—
73	C₂²×C₁₃	C₂×SD₃₂	1	4	yes	—
74	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
75	C₄×C₁₃	—	8	8	no	—
76	C₄×C₁₃	#500	1	2	yes	—
77	C₄×C₁₃	C₂×SD₃₂	1	8	yes	—
78	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
79	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
80	C₂²×Q₈	—	4	2	no	—
81	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
82	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
83	C₄⋊Q₈	—	2	8	no	—
84	C₄⋊Q₈	—	4	4	no	—
85	C₂×C₄⋊C₄	—	2	4	no	—
86	C₂×C₄⋊C₄	—	4	2	no	—
87	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
88	C₂×C₁₆	Q₈×C₁₃	1	8	yes	complemented
89	C₂×C₁₆	C₂³×C₁₃	1	4	yes	—
90	#107	—	2	8	no	—
91	#107	—	2	4	no	—
92	#107	C₂³×C₁₃	1	8	yes	—
93	C₄×C₈	D₄×C₁₃	1	2	yes	—
94	C₄×C₈	C₂³×C₁₃	1	2	yes	—
95	C₂×C₁₃	#2254	1	4	yes	direct product factor
96	C₂×C₁₃	C₂×#500	1	1	yes	characteristic
97	C₂×C₁₃	C₂²×SD₃₂	1	2	yes	—
98	C₂×Q₈	—	4	8	no	—
99	C₂×Q₈	—	8	8	no	—
100	C₂²×C₄	—	4	4	no	—
101	C₂²×C₄	C₁₃×D₈	1	2	yes	—
102	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
103	C₂×C₈	C₁₃×Q₁₆	1	4	yes	—
104	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
105	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
106	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
107	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
108	C₄⋊C₄	—	2	8	no	—
109	C₄⋊C₄	—	4	4	no	—
110	C₄⋊C₄	—	4	8	no	—
111	C₄²	C₁₃×D₈	1	2	yes	—
112	C₄²	C₂×D₄×C₁₃	1	2	yes	—
113	C₁₆	C₂×Q₈×C₁₃	1	8	yes	complemented
114	C₁₃	C₂×#2254	1	1	yes	characteristic, direct product factor, Sylow
115	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
116	Q₈	—	8	16	no	—
117	C₂×C₄	—	4	8	no	—
118	C₂×C₄	—	8	8	no	—
119	C₂×C₄	C₁₃×SD₃₂	1	8	yes	—
120	C₂×C₄	C₁₃×C₄⋊Q₈	1	2	yes	—
121	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
122	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
123	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
124	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
125	C₈	C₁₃×C₄⋊Q₈	1	2	yes	—
126	C₈	C₂×C₁₃×Q₁₆	1	4	yes	—
127	C₈	C₂²×Q₈×C₁₃	1	2	yes	—
128	C₂²	C₁₃×#500	1	2	yes	—
129	C₂²	C₂×C₁₃×SD₃₂	1	4	yes	—
130	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
131	C₄	—	8	8	no	—
132	C₄	C₁₃×#500	1	2	yes	—
133	C₄	C₂×C₁₃×SD₃₂	1	8	yes	—
134	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
135	C₄	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
136	C₂	C₁₃×#2254	1	4	yes	direct product factor
137	C₂	C₂×C₁₃×#500	1	1	yes	characteristic
138	C₂	C₂²×C₁₃×SD₃₂	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×#2254	C₂	direct (N × H)
22. C₂×C₁₃×C₁₆	Q₈	semidirect
29. C₂×#2254	C₁₃	direct (N × H)
45. C₁₃×C₁₆	C₂×Q₈	semidirect
47. #2254	C₂×C₁₃	direct (N × H)
88. C₂×C₁₆	Q₈×C₁₃	semidirect
95. C₂×C₁₃	#2254	direct (N × H)
113. C₁₆	C₂×Q₈×C₁₃	semidirect
114. C₁₃	C₂×#2254	direct (N × H)
136. C₂	C₁₃×#2254	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×#500	2
C₁₃×#2254	2
C₂×C₁₃×#367	2
C₂×C₄×C₁₃×C₁₆	2
C₂×#2254	13

Subgroups — C2×C13×#2254 #15720064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2254 #15720064