Subgroups — D₁₃×#1312 #15771904

Order 3328.

350 conjugacy classes of subgroups.

The subgroup lattice has 164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₆×D₁₃	C₂	1	2	yes	maximal
2	C₈²×D₁₃	C₂	1	1	yes	maximal, characteristic
3	#13112755	C₂	1	2	yes	maximal, complemented
4	#13112754	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1312	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₆×D₁₃	C₄	1	4	yes	—
7	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
8	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
9	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
10	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
11	C₈²×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₆×Dic₁₃	C₄	1	4	yes	—
13	C₄×#6090	C₂²	1	2	yes	—
14	C₈×#1055	C₄	1	1	yes	characteristic
15	C₈×#1055	C₄	1	1	yes	characteristic
16	C₈×#1055	C₂²	1	1	yes	characteristic
17	C₂×C₈×D₁₃	C₈	1	2	yes	—
18	C₂×C₈×D₁₃	C₈	1	2	yes	—
19	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
20	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
22	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
25	C₈×Dic₁₃	C₈	1	2	yes	—
26	C₈×Dic₁₃	C₈	1	2	yes	—
27	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
28	C₂×#6090	C₂×C₄	1	4	yes	—
29	C₄×#1055	C₂×C₄	1	1	yes	characteristic
30	C₄×#1055	C₂×C₄	1	1	yes	characteristic
31	C₄×#1055	C₂×C₄	1	1	yes	characteristic
32	C₁₆×D₁₃	—	2	8	no	—
33	C₂×#1312	—	13	1	no	maximal, Sylow
34	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
35	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
37	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
38	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
39	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
40	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
41	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
42	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
43	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
44	C₂×#1055	C₄²	1	2	yes	—
45	C₂×#1055	C₂×C₈	1	2	yes	—
46	C₂×#1055	C₂×C₈	1	2	yes	—
47	C₈×D₁₃	—	2	4	no	—
48	C₈×D₁₃	C₁₆	1	8	yes	complemented
49	C₈×D₁₃	M₁₆	1	8	yes	—
50	C₁₃×C₁₆	—	2	4	no	—
51	#6090	—	2	4	no	—
52	C₂×C₄×C₁₆	—	13	2	no	—
53	C₂×C₈²	—	13	1	no	—
54	#1312	—	13	2	no	—
55	#1312	—	13	1	no	—
56	#1312	D₁₃	1	1	yes	characteristic, direct product factor
57	C₂²×D₁₃	C₄×C₈	1	1	yes	characteristic
58	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
59	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
60	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
61	C₂×Dic₁₃	C₄×C₈	1	1	yes	characteristic
62	C₂×Dic₁₃	C₄×C₈	1	1	yes	characteristic
63	C₂×Dic₁₃	C₄×C₈	1	1	yes	characteristic
64	C₄×D₁₃	#97	1	4	yes	—
65	C₄×D₁₃	C₂×C₁₆	1	4	yes	—
66	C₄×D₁₃	M₃₂	1	4	yes	—
67	C₈×C₁₃	—	2	2	no	—
68	C₈×C₁₃	C₂×C₁₆	1	4	yes	complemented
69	C₈×C₁₃	C₂×M₁₆	1	4	yes	—
70	#1055	—	2	2	no	—
71	#1055	#97	1	4	yes	—
72	#1055	C₂×C₁₆	1	4	yes	complemented
73	C₂²×C₁₆	—	13	4	no	—
74	C₂×C₄×C₈	—	13	1	no	—
75	C₂×C₄×C₈	—	13	1	no	—
76	C₂×C₄×C₈	—	13	1	no	—
77	C₄×C₁₆	—	13	4	no	—
78	C₄×C₁₆	—	13	2	no	—
79	C₄×C₁₆	C₂×D₁₃	1	2	yes	—
80	C₈²	—	13	1	no	—
81	C₈²	—	13	1	no	—
82	C₈²	—	13	1	no	—
83	C₈²	C₂×D₁₃	1	1	yes	characteristic
84	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
85	C₂×D₁₃	#322	1	2	yes	—
86	C₂×D₁₃	C₄×C₁₆	1	2	yes	—
87	C₂×D₁₃	#346	1	2	yes	—
88	C₄×C₁₃	C₂×#97	1	2	yes	—
89	C₄×C₁₃	C₂²×C₁₆	1	2	yes	—
90	C₄×C₁₃	C₂×M₃₂	1	2	yes	—
91	Dic₁₃	#322	1	2	yes	—
92	Dic₁₃	C₄×C₁₆	1	2	yes	—
93	Dic₁₃	#346	1	2	yes	—
94	C₂²×C₈	—	13	2	no	—
95	C₂²×C₈	—	13	2	no	—
96	C₂²×C₈	—	13	2	no	—
97	C₂×C₄²	—	13	1	no	—
98	C₂×C₁₆	—	13	4	no	—
99	C₂×C₁₆	—	26	8	no	—
100	C₂×C₁₆	C₄×D₁₃	1	4	yes	—
101	C₄×C₈	—	13	2	no	—
102	C₄×C₈	—	13	2	no	—
103	C₄×C₈	—	13	2	no	—
104	C₄×C₈	—	13	1	no	—
105	C₄×C₈	—	13	1	no	—
106	C₄×C₈	—	13	1	no	—
107	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
108	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
109	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
110	C₂×C₁₃	C₂×#322	1	1	yes	characteristic
111	C₂×C₁₃	C₂×C₄×C₁₆	1	1	yes	characteristic
112	C₂×C₁₃	C₂×#346	1	1	yes	characteristic
113	D₁₃	#1312	1	4	yes	direct product factor
114	C₂²×C₄	—	13	1	no	—
115	C₂²×C₄	—	13	1	no	—
116	C₂²×C₄	—	13	1	no	—
117	C₂×C₈	—	13	2	no	—
118	C₂×C₈	—	13	2	no	—
119	C₂×C₈	—	13	8	no	—
120	C₂×C₈	—	13	8	no	—
121	C₂×C₈	—	13	2	no	—
122	C₂×C₈	—	26	4	no	—
123	C₂×C₈	C₈×D₁₃	1	2	yes	—
124	C₂×C₈	C₈×D₁₃	1	2	yes	—
125	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
126	C₄²	—	13	1	no	—
127	C₄²	—	13	1	no	—
128	C₄²	—	13	1	no	—
129	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
130	C₁₆	—	2	4	no	—
131	C₁₆	—	26	4	no	—
132	C₁₃	C₂×#1312	1	1	yes	characteristic, complemented, Sylow
133	C₂³	—	13	1	no	—
134	C₂×C₄	—	13	1	no	—
135	C₂×C₄	—	13	1	no	—
136	C₂×C₄	—	13	1	no	—
137	C₂×C₄	—	13	4	no	—
138	C₂×C₄	—	13	4	no	—
139	C₂×C₄	—	13	4	no	—
140	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
141	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
142	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
143	C₈	—	2	2	no	—
144	C₈	—	13	4	no	—
145	C₈	—	13	4	no	—
146	C₈	—	26	2	no	—
147	C₈	C₁₆×D₁₃	1	4	yes	complemented
148	C₈	M₁₆×D₁₃	1	4	yes	—
149	C₂²	—	13	2	no	—
150	C₂²	—	13	2	no	—
151	C₂²	—	13	2	no	—
152	C₂²	C₄×C₈×D₁₃	1	1	yes	characteristic
153	C₄	—	13	2	no	—
154	C₄	—	13	2	no	—
155	C₄	—	13	2	no	—
156	C₄	D₁₃×#97	1	2	yes	—
157	C₄	C₂×C₁₆×D₁₃	1	2	yes	—
158	C₄	D₁₃×M₃₂	1	2	yes	—
159	C₂	—	13	4	no	—
160	C₂	D₁₃×#322	1	1	yes	characteristic
161	C₂	C₄×C₁₆×D₁₃	1	1	yes	characteristic
162	C₂	D₁₃×#346	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄×C₈	C₂²×D₁₃
commutator	C₂×C₁₃	C₂×C₄×C₁₆
Fitting	C₁₃×#1312	C₂
socle	C₂²×C₁₃	C₂×C₄×C₈
prime radical	C₂²×D₁₃	C₄×C₈
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	#1312	D₁₃
hypocenter	C₁₃	C₂×#1312
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄×C₈ ◁ #1312

Complements

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

N	H ≅ G/N	type
3. #13112755	C₂	semidirect
4. #13112754	C₂	semidirect
5. C₁₃×#1312	C₂	semidirect
48. C₈×D₁₃	C₁₆	semidirect
56. #1312	D₁₃	direct (N × H)
68. C₈×C₁₃	C₂×C₁₆	semidirect
72. #1055	C₂×C₁₆	semidirect
113. D₁₃	#1312	direct (N × H)
132. C₁₃	C₂×#1312	semidirect
147. C₈	C₁₆×D₁₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₁₆×D₁₃	2
C₈²×D₁₃	2
#13112755	2
#13112754	2
C₁₃×#1312	2
C₂×#1312	13

Subgroups — D13×#1312 #15771904

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#1312 #15771904