Subgroups — C₁₃×#33726 #15720065

Order 3328.

490 conjugacy classes of subgroups.

The subgroup lattice has 172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3160	C₂	1	2	yes	maximal
2	C₁₃×#2254	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2253	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2252	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2158	C₂	1	4	yes	maximal
6	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#533	—	2	2	no	—
8	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
9	C₁₃×#500	C₂²	1	4	yes	—
10	C₁₃×#499	—	2	2	no	—
11	C₁₃×#499	C₂²	1	4	yes	—
12	C₁₃×#498	—	2	2	no	—
13	C₁₃×#427	—	2	2	no	—
14	C₁₃×#427	C₂²	1	4	yes	—
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#367	C₂²	1	8	yes	—
17	C₁₃×#366	C₂²	1	8	yes	—
18	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
19	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
20	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
23	C₁₃×C₄⋊Q₈	—	2	4	no	—
24	C₁₃×#125	—	2	4	no	—
25	C₁₃×C₂²⋊Q₈	—	4	4	no	—
26	C₄×Q₈×C₁₃	—	4	4	no	—
27	C₁₃×#117	—	2	4	no	—
28	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
29	C₂×C₁₃×C₁₆	Q₈	1	8	yes	complemented
30	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
31	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
32	C₁₃×#107	—	2	4	no	—
33	C₁₃×#107	C₂³	1	8	yes	—
34	C₁₃×#106	—	2	4	no	—
35	C₁₃×#106	—	2	4	no	—
36	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
37	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
38	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
39	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
40	#33726	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂×Q₈×C₁₃	—	4	4	no	—
42	C₂²×C₄×C₁₃	D₈	1	2	yes	—
43	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₈×C₁₃	Q₁₆	1	4	yes	—
45	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
48	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
49	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
50	C₁₃×C₄⋊C₄	—	2	8	no	—
51	C₁₃×C₄⋊C₄	—	4	8	no	—
52	C₁₃×C₄⋊C₄	—	4	4	no	—
53	C₁₃×C₂²⋊C₄	—	4	4	no	—
54	C₄²×C₁₃	—	4	4	no	—
55	C₄²×C₁₃	D₈	1	2	yes	—
56	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
57	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
58	C₁₃×C₁₆	C₂×Q₈	1	4	yes	—
59	C₁₃×C₁₆	C₂×Q₈	1	4	yes	—
60	#3160	C₂×C₁₃	1	2	yes	—
61	#2254	C₂×C₁₃	1	2	yes	complemented
62	#2253	C₂×C₁₃	1	4	yes	complemented
63	#2252	C₂×C₁₃	1	2	yes	complemented
64	#2158	C₂×C₁₃	1	4	yes	—
65	C₂×C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic
66	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
67	Q₈×C₁₃	—	8	8	no	—
68	C₂×C₄×C₁₃	—	2	4	no	—
69	C₂×C₄×C₁₃	—	4	8	no	—
70	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
71	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
72	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
73	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
74	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
75	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
76	C₈×C₁₃	C₄⋊Q₈	1	2	yes	—
77	C₈×C₁₃	C₂×Q₁₆	1	2	yes	—
78	C₈×C₁₃	C₂×Q₁₆	1	2	yes	—
79	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
80	#533	—	2	2	no	—
81	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
82	#500	C₂²×C₁₃	1	4	yes	—
83	#499	—	2	2	no	—
84	#499	C₂²×C₁₃	1	4	yes	—
85	#498	—	2	2	no	—
86	#427	—	2	2	no	—
87	#427	C₂²×C₁₃	1	4	yes	—
88	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
89	#367	C₂²×C₁₃	1	8	yes	—
90	#366	C₂²×C₁₃	1	8	yes	—
91	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
92	C₄×C₁₆	C₂²×C₁₃	1	2	yes	—
93	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
94	C₂²×C₁₃	—	2	2	no	—
95	C₂²×C₁₃	#500	1	2	yes	—
96	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
97	C₄×C₁₃	—	2	2	no	—
98	C₄×C₁₃	—	8	8	no	—
99	C₄×C₁₃	#500	1	2	yes	—
100	C₄×C₁₃	#508	1	4	yes	—
101	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
102	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
103	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
104	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
105	C₄⋊Q₈	—	2	4	no	—
106	#125	—	2	4	no	—
107	C₂²⋊Q₈	—	4	4	no	—
108	C₄×Q₈	—	4	4	no	—
109	#117	—	2	4	no	—
110	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
111	C₂×C₁₆	Q₈×C₁₃	1	8	yes	complemented
112	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
113	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
114	#107	—	2	4	no	—
115	#107	C₂³×C₁₃	1	8	yes	—
116	#106	—	2	4	no	—
117	#106	—	2	4	no	—
118	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
119	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
120	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
121	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
122	C₂×C₁₃	—	2	2	no	—
123	C₂×C₁₃	C₂×#500	1	1	yes	characteristic
124	C₂×C₁₃	C₂×#508	1	2	yes	—
125	C₂×Q₈	—	4	4	no	—
126	C₂²×C₄	C₁₃×D₈	1	2	yes	—
127	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
128	C₂×C₈	C₁₃×Q₁₆	1	4	yes	—
129	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
130	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
131	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
132	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
133	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
134	C₄⋊C₄	—	2	8	no	—
135	C₄⋊C₄	—	4	8	no	—
136	C₄⋊C₄	—	4	4	no	—
137	C₂²⋊C₄	—	4	4	no	—
138	C₄²	—	4	4	no	—
139	C₄²	C₁₃×D₈	1	2	yes	—
140	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
141	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
142	C₁₆	C₂×Q₈×C₁₃	1	4	yes	—
143	C₁₆	C₂×Q₈×C₁₃	1	4	yes	—
144	C₁₃	#33726	1	1	yes	characteristic, direct product factor, Sylow
145	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
146	Q₈	—	8	8	no	—
147	C₂×C₄	—	2	4	no	—
148	C₂×C₄	—	4	8	no	—
149	C₂×C₄	C₁₃×C₄⋊Q₈	1	2	yes	—
150	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
151	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
152	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
153	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
154	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
155	C₈	C₁₃×C₄⋊Q₈	1	2	yes	—
156	C₈	C₂×C₁₃×Q₁₆	1	2	yes	—
157	C₈	C₂×C₁₃×Q₁₆	1	2	yes	—
158	C₈	C₂²×Q₈×C₁₃	1	2	yes	—
159	C₂²	—	2	2	no	—
160	C₂²	C₁₃×#500	1	2	yes	—
161	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
162	C₄	—	2	2	no	—
163	C₄	—	8	8	no	—
164	C₄	C₁₃×#500	1	2	yes	—
165	C₄	C₁₃×#508	1	4	yes	—
166	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
167	C₄	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
168	C₂	—	2	2	no	—
169	C₂	C₂×C₁₃×#500	1	1	yes	characteristic
170	C₂	C₂×C₁₃×#508	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂²×D₈
prime radical	C₂³×C₁₃	C₂×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×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	semidirect
3. C₁₃×#2253	C₂	semidirect
4. C₁₃×#2252	C₂	semidirect
29. C₂×C₁₃×C₁₆	Q₈	semidirect
40. #33726	C₁₃	direct (N × H)
61. #2254	C₂×C₁₃	semidirect
62. #2253	C₂×C₁₃	semidirect
63. #2252	C₂×C₁₃	semidirect
111. C₂×C₁₆	Q₈×C₁₃	semidirect
144. C₁₃	#33726	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×#3160	2
C₁₃×#2254	2
C₁₃×#2253	2
C₁₃×#2252	2
C₁₃×#2158	2
C₂×C₄×C₁₃×C₁₆	2
#33726	13

Subgroups — C13×#33726 #15720065

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33726 #15720065