Subgroups — C₁₃×#3383 #13112441

Order 1664.

324 conjugacy classes of subgroups.

The subgroup lattice has 154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#557	C₂	1	2	yes	maximal
2	C₁₃×#500	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#499	C₂	1	2	yes	maximal
4	C₁₃×#479	C₂	1	4	yes	maximal
5	C₁₃×#475	C₂	1	2	yes	maximal
6	C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
7	C₄×C₁₃×Q₁₆	C₂	1	2	yes	maximal
8	C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
10	C₁₃×C₄⋊Q₈	—	2	2	no	—
11	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
12	C₁₃×#125	—	2	4	no	—
13	C₁₃×#125	C₂²	1	4	yes	—
14	C₄×Q₈×C₁₃	—	2	2	no	—
15	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
16	C₄×Q₈×C₁₃	C₂²	1	4	yes	—
17	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
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×#103	C₂²	1	4	yes	—
25	C₁₃×#103	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×Q₈×C₁₃	C₂³	1	2	yes	—
31	C₁₃×Q₁₆	Q₈	1	4	yes	complemented
32	C₂×C₈×C₁₃	C₂³	1	2	yes	—
33	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
34	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
35	C₁₃×C₄⋊C₄	—	2	4	no	—
36	C₁₃×C₄⋊C₄	—	2	2	no	—
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	C₄²×C₁₃	—	2	4	no	—
45	C₄²×C₁₃	—	2	2	no	—
46	C₄²×C₁₃	C₂³	1	2	yes	—
47	C₄²×C₁₃	C₂³	1	1	yes	characteristic
48	#3383	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	Q₈×C₁₃	—	2	2	no	—
50	Q₈×C₁₃	—	2	2	no	—
51	Q₈×C₁₃	—	4	4	no	—
52	Q₈×C₁₃	C₂×Q₈	1	4	yes	—
53	C₂×C₄×C₁₃	—	2	2	no	—
54	C₂×C₄×C₁₃	—	2	2	no	—
55	C₂×C₄×C₁₃	—	2	4	no	—
56	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
57	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
58	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
59	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
60	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
61	C₈×C₁₃	—	2	2	no	—
62	C₈×C₁₃	—	2	1	no	—
63	C₈×C₁₃	C₂×Q₈	1	2	yes	—
64	#557	C₂×C₁₃	1	2	yes	—
65	#500	C₂×C₁₃	1	1	yes	characteristic
66	#499	C₂×C₁₃	1	2	yes	—
67	#479	C₂×C₁₃	1	4	yes	—
68	#475	C₂×C₁₃	1	2	yes	—
69	C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic
70	C₄×Q₁₆	C₂×C₁₃	1	2	yes	—
71	C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic
72	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
73	C₄×C₁₃	—	2	4	no	—
74	C₄×C₁₃	—	2	2	no	—
75	C₄×C₁₃	—	2	2	no	—
76	C₄×C₁₃	—	2	1	no	—
77	C₄×C₁₃	—	4	4	no	—
78	C₄×C₁₃	—	4	2	no	—
79	C₄×C₁₃	#135	1	2	yes	—
80	C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
81	C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
82	C₂×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
83	C₄⋊Q₈	—	2	2	no	—
84	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
85	#125	—	2	4	no	—
86	#125	C₂²×C₁₃	1	4	yes	—
87	C₄×Q₈	—	2	2	no	—
88	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
89	C₄×Q₈	C₂²×C₁₃	1	4	yes	—
90	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
91	#107	C₂²×C₁₃	1	1	yes	characteristic
92	#107	C₂²×C₁₃	1	2	yes	—
93	#107	C₂²×C₁₃	1	2	yes	—
94	#106	C₂²×C₁₃	1	4	yes	—
95	C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
96	C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
97	#103	C₂²×C₁₃	1	4	yes	—
98	#103	C₂²×C₁₃	1	2	yes	—
99	C₄×C₈	C₂²×C₁₃	1	2	yes	—
100	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
101	C₂×C₁₃	D₄×Q₈	1	1	yes	characteristic
102	C₂×C₁₃	C₂×#135	1	1	yes	characteristic
103	C₂×C₁₃	#578	1	1	yes	characteristic
104	C₂×Q₈	—	2	2	no	—
105	C₂×Q₈	D₄×C₁₃	1	1	yes	characteristic
106	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
107	Q₁₆	Q₈×C₁₃	1	4	yes	complemented
108	C₂×C₈	C₂³×C₁₃	1	2	yes	—
109	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
110	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
111	C₄⋊C₄	—	2	4	no	—
112	C₄⋊C₄	—	2	2	no	—
113	C₄⋊C₄	—	2	4	no	—
114	C₄⋊C₄	—	2	2	no	—
115	C₄⋊C₄	—	2	4	no	—
116	C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
117	C₄⋊C₄	D₄×C₁₃	1	2	yes	—
118	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
119	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
120	C₄²	—	2	4	no	—
121	C₄²	—	2	2	no	—
122	C₄²	C₂³×C₁₃	1	2	yes	—
123	C₄²	C₂³×C₁₃	1	1	yes	characteristic
124	C₁₃	#3383	1	1	yes	characteristic, direct product factor, Sylow
125	Q₈	—	2	2	no	—
126	Q₈	—	2	2	no	—
127	Q₈	—	4	4	no	—
128	Q₈	C₂×Q₈×C₁₃	1	4	yes	—
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	2	2	no	—
131	C₂×C₄	—	2	4	no	—
132	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
133	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
134	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
135	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
136	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
137	C₈	—	2	2	no	—
138	C₈	—	2	1	no	—
139	C₈	C₂×Q₈×C₁₃	1	2	yes	—
140	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
141	C₄	—	2	4	no	—
142	C₄	—	2	2	no	—
143	C₄	—	2	2	no	—
144	C₄	—	2	1	no	—
145	C₄	—	4	4	no	—
146	C₄	—	4	2	no	—
147	C₄	C₁₃×#135	1	2	yes	—
148	C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
149	C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
150	C₂	D₄×Q₈×C₁₃	1	1	yes	characteristic
151	C₂	C₂×C₁₃×#135	1	1	yes	characteristic
152	C₂	C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
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
31. C₁₃×Q₁₆	Q₈	semidirect
48. #3383	C₁₃	direct (N × H)
107. Q₁₆	Q₈×C₁₃	semidirect
124. C₁₃	#3383	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×#557	2
C₁₃×#500	2
C₁₃×#499	2
C₁₃×#479	2
C₁₃×#475	2
C₈×Q₈×C₁₃	2
C₄×C₁₃×Q₁₆	2
#3383	13

Subgroups — C13×#3383 #13112441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3383 #13112441