Subgroups — C₁₃×#3390 #13112448

Order 1664.

320 conjugacy classes of subgroups.

The subgroup lattice has 182 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×#501	C₂	1	2	yes	maximal
3	C₁₃×#499	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#479	C₂	1	2	yes	maximal
5	C₁₃×#479	C₂	1	2	yes	maximal
6	C₁₃×#477	C₂	1	2	yes	maximal
7	C₁₃×#446	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#441	C₂	1	2	yes	maximal
9	C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
11	C₁₃×C₄⋊Q₈	—	2	2	no	—
12	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
13	C₁₃×#125	—	2	2	no	—
14	C₁₃×#125	—	2	2	no	—
15	C₁₃×#125	C₂²	1	2	yes	—
16	C₁₃×#125	C₂²	1	2	yes	—
17	C₄×Q₈×C₁₃	—	2	2	no	—
18	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
19	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
20	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
21	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#107	C₂²	1	1	yes	characteristic
23	C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₁₃×#107	C₂²	1	2	yes	—
25	C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₁₃×#106	C₂²	1	2	yes	—
27	C₁₃×#106	C₂²	1	2	yes	—
28	C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
29	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₁₃×#103	C₂²	1	2	yes	—
31	C₁₃×#103	C₂²	1	2	yes	—
32	C₁₃×#103	C₂²	1	2	yes	—
33	C₁₃×#97	C₂²	1	2	yes	—
34	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×Q₈×C₁₃	—	2	2	no	—
36	C₂×Q₈×C₁₃	D₄	1	1	yes	characteristic
37	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
38	C₁₃×Q₁₆	Q₈	1	4	yes	complemented
39	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
40	C₂×C₈×C₁₃	C₂³	1	2	yes	—
41	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
42	C₁₃×C₄⋊C₄	—	2	2	no	—
43	C₁₃×C₄⋊C₄	—	2	2	no	—
44	C₁₃×C₄⋊C₄	—	2	2	no	—
45	C₁₃×C₄⋊C₄	—	2	2	no	—
46	C₁₃×C₄⋊C₄	—	2	2	no	—
47	C₁₃×C₄⋊C₄	—	2	2	no	—
48	C₁₃×C₄⋊C₄	—	2	2	no	—
49	C₁₃×C₄⋊C₄	—	2	2	no	—
50	C₁₃×C₄⋊C₄	D₄	1	2	yes	—
51	C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
52	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
53	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
54	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
55	C₄²×C₁₃	—	2	2	no	—
56	C₄²×C₁₃	—	2	2	no	—
57	C₄²×C₁₃	—	2	2	no	—
58	C₄²×C₁₃	C₂³	1	1	yes	characteristic
59	C₄²×C₁₃	C₂³	1	2	yes	—
60	#3390	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	Q₈×C₁₃	—	2	2	no	—
62	Q₈×C₁₃	—	4	1	no	—
63	Q₈×C₁₃	—	4	4	no	—
64	Q₈×C₁₃	C₂×Q₈	1	4	yes	—
65	C₂×C₄×C₁₃	—	2	2	no	—
66	C₂×C₄×C₁₃	—	2	2	no	—
67	C₂×C₄×C₁₃	—	2	2	no	—
68	C₂×C₄×C₁₃	—	2	2	no	—
69	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
71	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
72	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
73	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
74	C₈×C₁₃	—	2	1	no	—
75	C₈×C₁₃	—	2	2	no	—
76	C₈×C₁₃	C₂×Q₈	1	2	yes	—
77	#557	C₂×C₁₃	1	2	yes	—
78	#501	C₂×C₁₃	1	2	yes	—
79	#499	C₂×C₁₃	1	1	yes	characteristic
80	#479	C₂×C₁₃	1	2	yes	—
81	#479	C₂×C₁₃	1	2	yes	—
82	#477	C₂×C₁₃	1	2	yes	—
83	#446	C₂×C₁₃	1	1	yes	characteristic
84	#441	C₂×C₁₃	1	2	yes	—
85	C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic
86	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
87	C₄×C₁₃	—	2	4	no	—
88	C₄×C₁₃	—	2	1	no	—
89	C₄×C₁₃	—	2	2	no	—
90	C₄×C₁₃	—	2	1	no	—
91	C₄×C₁₃	—	2	2	no	—
92	C₄×C₁₃	—	4	2	no	—
93	C₄×C₁₃	—	4	2	no	—
94	C₄×C₁₃	—	4	2	no	—
95	C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
96	C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
97	C₂×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
98	C₄⋊Q₈	—	2	2	no	—
99	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
100	#125	—	2	2	no	—
101	#125	—	2	2	no	—
102	#125	C₂²×C₁₃	1	2	yes	—
103	#125	C₂²×C₁₃	1	2	yes	—
104	C₄×Q₈	—	2	2	no	—
105	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
106	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
107	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
108	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
109	#107	C₂²×C₁₃	1	1	yes	characteristic
110	#107	C₂²×C₁₃	1	1	yes	characteristic
111	#107	C₂²×C₁₃	1	2	yes	—
112	#107	C₂²×C₁₃	1	1	yes	characteristic
113	#106	C₂²×C₁₃	1	2	yes	—
114	#106	C₂²×C₁₃	1	2	yes	—
115	C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
116	C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
117	#103	C₂²×C₁₃	1	2	yes	—
118	#103	C₂²×C₁₃	1	2	yes	—
119	#103	C₂²×C₁₃	1	2	yes	—
120	#97	C₂²×C₁₃	1	2	yes	—
121	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
122	C₂×C₁₃	D₄×Q₈	1	1	yes	characteristic
123	C₂×C₁₃	#575	1	1	yes	characteristic
124	C₂×C₁₃	#578	1	1	yes	characteristic
125	C₂×Q₈	—	2	2	no	—
126	C₂×Q₈	D₄×C₁₃	1	1	yes	characteristic
127	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
128	Q₁₆	Q₈×C₁₃	1	4	yes	complemented
129	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
130	C₂×C₈	C₂³×C₁₃	1	2	yes	—
131	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
132	C₄⋊C₄	—	2	2	no	—
133	C₄⋊C₄	—	2	2	no	—
134	C₄⋊C₄	—	2	2	no	—
135	C₄⋊C₄	—	2	2	no	—
136	C₄⋊C₄	—	2	2	no	—
137	C₄⋊C₄	—	2	2	no	—
138	C₄⋊C₄	—	2	2	no	—
139	C₄⋊C₄	—	2	2	no	—
140	C₄⋊C₄	D₄×C₁₃	1	2	yes	—
141	C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
142	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
143	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
144	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
145	C₄²	—	2	2	no	—
146	C₄²	—	2	2	no	—
147	C₄²	—	2	2	no	—
148	C₄²	C₂³×C₁₃	1	1	yes	characteristic
149	C₄²	C₂³×C₁₃	1	2	yes	—
150	C₁₃	#3390	1	1	yes	characteristic, direct product factor, Sylow
151	Q₈	—	2	2	no	—
152	Q₈	—	4	1	no	—
153	Q₈	—	4	4	no	—
154	Q₈	C₂×Q₈×C₁₃	1	4	yes	—
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
160	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
161	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
162	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
163	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
164	C₈	—	2	1	no	—
165	C₈	—	2	2	no	—
166	C₈	C₂×Q₈×C₁₃	1	2	yes	—
167	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
168	C₄	—	2	4	no	—
169	C₄	—	2	1	no	—
170	C₄	—	2	2	no	—
171	C₄	—	2	1	no	—
172	C₄	—	2	2	no	—
173	C₄	—	4	2	no	—
174	C₄	—	4	2	no	—
175	C₄	—	4	2	no	—
176	C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
177	C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
178	C₂	D₄×Q₈×C₁₃	1	1	yes	characteristic
179	C₂	C₁₃×#575	1	1	yes	characteristic
180	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
38. C₁₃×Q₁₆	Q₈	semidirect
60. #3390	C₁₃	direct (N × H)
128. Q₁₆	Q₈×C₁₃	semidirect
150. C₁₃	#3390	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×#501	2
C₁₃×#499	2
C₁₃×#479	2
C₁₃×#477	2
C₁₃×#446	2
C₁₃×#441	2
C₄×C₁₃×Q₁₆	2
#3390	13

Subgroups — C13×#3390 #13112448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3390 #13112448