Subgroups — C₁₃×#3380 #13112438

Order 1664.

352 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	C₁₃×#554	C₂	1	2	yes	maximal, complemented
2	C₁₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#499	C₂	1	2	yes	maximal, complemented
4	C₁₃×#478	C₂	1	4	yes	maximal, complemented
5	C₁₃×#476	C₂	1	2	yes	maximal, complemented
6	C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₁₃×D₈	C₂	1	2	yes	maximal
8	C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₃×D₈	C₂²	1	1	yes	characteristic
10	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
11	C₁₃×#125	C₂²	1	4	yes	—
12	C₁₃×C₂²⋊Q₈	—	2	2	no	—
13	C₁₃×C₂²⋊Q₈	—	2	4	no	—
14	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₄×D₄×C₁₃	C₂²	1	2	yes	—
16	C₄×D₄×C₁₃	C₂²	1	4	yes	—
17	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
18	C₁₃×#107	C₂²	1	1	yes	characteristic
19	C₁₃×#107	C₂²	1	2	yes	—
20	C₁₃×#107	C₂²	1	2	yes	—
21	C₁₃×#106	C₂²	1	4	yes	—
22	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
24	C₁₃×#102	C₂²	1	4	yes	—
25	C₁₃×#102	C₂²	1	2	yes	—
26	C₄×C₈×C₁₃	C₂²	1	2	yes	—
27	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×Q₈×C₁₃	—	2	2	no	—
29	C₂×Q₈×C₁₃	D₄	1	1	yes	characteristic
30	C₂×D₄×C₁₃	C₂³	1	2	yes	—
31	C₂²×C₄×C₁₃	—	2	2	no	—
32	C₂²×C₄×C₁₃	—	2	4	no	—
33	C₁₃×D₈	Q₈	1	4	yes	complemented
34	C₂×C₈×C₁₃	C₂³	1	2	yes	—
35	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
36	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
37	C₁₃×C₄⋊C₄	—	2	4	no	—
38	C₁₃×C₄⋊C₄	—	2	2	no	—
39	C₁₃×C₄⋊C₄	—	2	4	no	—
40	C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
41	C₁₃×C₄⋊C₄	D₄	1	2	yes	—
42	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
43	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
44	C₁₃×C₂²⋊C₄	—	2	2	no	—
45	C₁₃×C₂²⋊C₄	—	2	4	no	—
46	C₄²×C₁₃	C₂³	1	2	yes	—
47	C₄²×C₁₃	C₂³	1	1	yes	characteristic
48	#3380	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂³×C₁₃	—	2	2	no	—
50	Q₈×C₁₃	—	2	2	no	—
51	Q₈×C₁₃	—	8	2	no	—
52	D₄×C₁₃	—	2	2	no	—
53	D₄×C₁₃	C₂×Q₈	1	4	yes	—
54	C₂×C₄×C₁₃	—	2	2	no	—
55	C₂×C₄×C₁₃	—	2	4	no	—
56	C₂×C₄×C₁₃	—	4	4	no	—
57	C₂×C₄×C₁₃	—	8	4	no	—
58	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
59	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
60	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
61	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
62	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
63	C₈×C₁₃	—	2	2	no	—
64	C₈×C₁₃	—	2	1	no	—
65	C₈×C₁₃	C₂×Q₈	1	2	yes	—
66	#554	C₂×C₁₃	1	2	yes	complemented
67	#500	C₂×C₁₃	1	1	yes	characteristic, complemented
68	#499	C₂×C₁₃	1	2	yes	complemented
69	#478	C₂×C₁₃	1	4	yes	complemented
70	#476	C₂×C₁₃	1	2	yes	complemented
71	C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
72	C₄×D₈	C₂×C₁₃	1	2	yes	—
73	C₄×D₈	C₂×C₁₃	1	1	yes	characteristic
74	C₂²×C₁₃	—	2	4	no	—
75	C₂²×C₁₃	—	4	2	no	—
76	C₂²×C₁₃	—	4	2	no	—
77	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
78	C₄×C₁₃	—	2	2	no	—
79	C₄×C₁₃	—	2	2	no	—
80	C₄×C₁₃	—	2	1	no	—
81	C₄×C₁₃	—	4	2	no	—
82	C₄×C₁₃	—	4	4	no	—
83	C₄×C₁₃	#135	1	2	yes	—
84	C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
85	C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
86	C₂×D₈	C₂²×C₁₃	1	1	yes	characteristic
87	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
88	#125	C₂²×C₁₃	1	4	yes	—
89	C₂²⋊Q₈	—	2	2	no	—
90	C₂²⋊Q₈	—	2	4	no	—
91	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
92	C₄×D₄	C₂²×C₁₃	1	2	yes	—
93	C₄×D₄	C₂²×C₁₃	1	4	yes	—
94	C₂×C₄⋊C₄	—	2	2	no	—
95	#107	C₂²×C₁₃	1	1	yes	characteristic
96	#107	C₂²×C₁₃	1	2	yes	—
97	#107	C₂²×C₁₃	1	2	yes	—
98	#106	C₂²×C₁₃	1	4	yes	—
99	C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
100	C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
101	#102	C₂²×C₁₃	1	4	yes	—
102	#102	C₂²×C₁₃	1	2	yes	—
103	C₄×C₈	C₂²×C₁₃	1	2	yes	—
104	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
105	C₂×C₁₃	—	4	4	no	—
106	C₂×C₁₃	D₄×Q₈	1	1	yes	characteristic
107	C₂×C₁₃	C₂×#135	1	1	yes	characteristic
108	C₂×C₁₃	#576	1	1	yes	characteristic
109	C₂×Q₈	—	2	2	no	—
110	C₂×Q₈	D₄×C₁₃	1	1	yes	characteristic
111	C₂×D₄	C₂³×C₁₃	1	2	yes	—
112	C₂²×C₄	—	2	2	no	—
113	C₂²×C₄	—	2	4	no	—
114	D₈	Q₈×C₁₃	1	4	yes	complemented
115	C₂×C₈	C₂³×C₁₃	1	2	yes	—
116	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
117	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
118	C₄⋊C₄	—	2	4	no	—
119	C₄⋊C₄	—	2	2	no	—
120	C₄⋊C₄	—	2	4	no	—
121	C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
122	C₄⋊C₄	D₄×C₁₃	1	2	yes	—
123	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
124	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
125	C₂²⋊C₄	—	2	2	no	—
126	C₂²⋊C₄	—	2	4	no	—
127	C₄²	C₂³×C₁₃	1	2	yes	—
128	C₄²	C₂³×C₁₃	1	1	yes	characteristic
129	C₁₃	#3380	1	1	yes	characteristic, direct product factor, Sylow
130	C₂³	—	2	2	no	—
131	Q₈	—	2	2	no	—
132	Q₈	—	8	2	no	—
133	D₄	—	2	2	no	—
134	D₄	C₂×Q₈×C₁₃	1	4	yes	—
135	C₂×C₄	—	2	2	no	—
136	C₂×C₄	—	2	4	no	—
137	C₂×C₄	—	4	4	no	—
138	C₂×C₄	—	8	4	no	—
139	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
140	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
141	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
142	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
143	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
144	C₈	—	2	2	no	—
145	C₈	—	2	1	no	—
146	C₈	C₂×Q₈×C₁₃	1	2	yes	—
147	C₂²	—	2	4	no	—
148	C₂²	—	4	2	no	—
149	C₂²	—	4	2	no	—
150	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
151	C₄	—	2	2	no	—
152	C₄	—	2	2	no	—
153	C₄	—	2	1	no	—
154	C₄	—	4	2	no	—
155	C₄	—	4	4	no	—
156	C₄	C₁₃×#135	1	2	yes	—
157	C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
158	C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
159	C₂	—	4	4	no	—
160	C₂	D₄×Q₈×C₁₃	1	1	yes	characteristic
161	C₂	C₂×C₁₃×#135	1	1	yes	characteristic
162	C₂	C₁₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#554	C₂	semidirect
2. C₁₃×#500	C₂	semidirect
3. C₁₃×#499	C₂	semidirect
4. C₁₃×#478	C₂	semidirect
5. C₁₃×#476	C₂	semidirect
6. C₈×Q₈×C₁₃	C₂	semidirect
33. C₁₃×D₈	Q₈	semidirect
48. #3380	C₁₃	direct (N × H)
66. #554	C₂×C₁₃	semidirect
67. #500	C₂×C₁₃	semidirect
68. #499	C₂×C₁₃	semidirect
69. #478	C₂×C₁₃	semidirect
70. #476	C₂×C₁₃	semidirect
71. C₈×Q₈	C₂×C₁₃	semidirect
114. D₈	Q₈×C₁₃	semidirect
129. C₁₃	#3380	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×#554	2
C₁₃×#500	2
C₁₃×#499	2
C₁₃×#478	2
C₁₃×#476	2
C₈×Q₈×C₁₃	2
C₄×C₁₃×D₈	2
#3380	13

Subgroups — C13×#3380 #13112438

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3380 #13112438