Subgroups — C₁₃×#2605 #13111663

Order 1664.

396 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#400	C₂	1	2	yes	maximal
2	C₁₃×#395	C₂	1	2	yes	maximal
3	C₁₃×#391	C₂	1	2	yes	maximal
4	C₁₃×#391	C₂	1	2	yes	maximal
5	C₁₃×#387	C₂	1	2	yes	maximal
6	C₁₃×#387	C₂	1	2	yes	maximal
7	C₁₃×#383	C₂	1	1	yes	maximal, characteristic
8	C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#376	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₈×C₁₃	C₂²	1	2	yes	—
11	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
16	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#95	C₂²	1	2	yes	—
20	C₁₃×#95	C₂²	1	1	yes	characteristic
21	C₁₃×#95	C₂²	1	2	yes	—
22	C₁₃×#95	C₂²	1	1	yes	characteristic
23	C₁₃×#95	C₂²	1	2	yes	—
24	C₁₃×#95	C₂²	1	2	yes	—
25	C₁₃×#95	C₂²	1	2	yes	—
26	C₁₃×#95	C₂²	1	2	yes	—
27	C₁₃×#95	C₂²	1	2	yes	—
28	C₁₃×#95	C₂²	1	2	yes	—
29	C₁₃×#95	C₂²	1	1	yes	characteristic
30	C₁₃×#95	C₂²	1	1	yes	characteristic
31	C₂×Q₈×C₁₃	—	2	4	no	—
32	C₂×Q₈×C₁₃	—	2	4	no	—
33	C₂×Q₈×C₁₃	—	4	2	no	—
34	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
35	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
36	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
37	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
38	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
39	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
42	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
43	C₁₃×C₄⋊C₄	—	2	4	no	—
44	C₁₃×C₄⋊C₄	—	2	4	no	—
45	C₁₃×C₄⋊C₄	—	2	4	no	—
46	C₁₃×C₄⋊C₄	—	4	2	no	—
47	C₄²×C₁₃	—	2	4	no	—
48	C₄²×C₁₃	—	4	1	no	—
49	C₄²×C₁₃	—	4	1	no	—
50	C₄²×C₁₃	Q₈	1	4	yes	complemented
51	#2605	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
52	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
53	Q₈×C₁₃	—	4	8	no	—
54	C₂×C₄×C₁₃	—	2	2	no	—
55	C₂×C₄×C₁₃	—	2	2	no	—
56	C₂×C₄×C₁₃	—	2	2	no	—
57	C₂×C₄×C₁₃	—	2	2	no	—
58	C₂×C₄×C₁₃	—	2	1	no	—
59	C₂×C₄×C₁₃	—	2	2	no	—
60	C₂×C₄×C₁₃	—	2	2	no	—
61	C₂×C₄×C₁₃	—	2	1	no	—
62	C₂×C₄×C₁₃	—	2	2	no	—
63	C₂×C₄×C₁₃	—	2	2	no	—
64	C₂×C₄×C₁₃	—	2	2	no	—
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	—	2	2	no	—
70	C₂×C₄×C₁₃	—	2	2	no	—
71	C₂×C₄×C₁₃	—	2	2	no	—
72	C₂×C₄×C₁₃	—	2	2	no	—
73	C₂×C₄×C₁₃	—	2	2	no	—
74	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
75	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
76	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
77	C₂×C₄×C₁₃	#41	1	4	yes	—
78	C₂×C₄×C₁₃	#41	1	4	yes	—
79	#400	C₂×C₁₃	1	2	yes	—
80	#395	C₂×C₁₃	1	2	yes	—
81	#391	C₂×C₁₃	1	2	yes	—
82	#391	C₂×C₁₃	1	2	yes	—
83	#387	C₂×C₁₃	1	2	yes	—
84	#387	C₂×C₁₃	1	2	yes	—
85	#383	C₂×C₁₃	1	1	yes	characteristic
86	C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
87	#376	C₂×C₁₃	1	1	yes	characteristic
88	C₂²×C₁₃	C₂²×Q₈	1	1	yes	characteristic
89	C₂²×C₁₃	C₂×#41	1	2	yes	—
90	C₂²×C₁₃	C₂×#41	1	2	yes	—
91	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
92	C₂²×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
93	C₄×C₁₃	—	2	2	no	—
94	C₄×C₁₃	—	2	2	no	—
95	C₄×C₁₃	—	2	2	no	—
96	C₄×C₁₃	—	2	4	no	—
97	C₄×C₁₃	—	2	4	no	—
98	C₄×C₁₃	—	4	2	no	—
99	C₄×C₁₃	—	4	2	no	—
100	C₄×C₁₃	—	4	2	no	—
101	C₄×C₁₃	—	4	2	no	—
102	C₂²×Q₈	C₂²×C₁₃	1	2	yes	—
103	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
104	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
105	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
106	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
107	C₂×C₄²	C₂²×C₁₃	1	2	yes	—
108	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
109	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
110	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
111	#95	C₂²×C₁₃	1	2	yes	—
112	#95	C₂²×C₁₃	1	1	yes	characteristic
113	#95	C₂²×C₁₃	1	1	yes	characteristic
114	#95	C₂²×C₁₃	1	2	yes	—
115	#95	C₂²×C₁₃	1	1	yes	characteristic
116	#95	C₂²×C₁₃	1	2	yes	—
117	#95	C₂²×C₁₃	1	1	yes	characteristic
118	#95	C₂²×C₁₃	1	2	yes	—
119	#95	C₂²×C₁₃	1	2	yes	—
120	#95	C₂²×C₁₃	1	2	yes	—
121	#95	C₂²×C₁₃	1	2	yes	—
122	#95	C₂²×C₁₃	1	2	yes	—
123	C₂×C₁₃	#533	1	1	yes	characteristic
124	C₂×C₁₃	#533	1	1	yes	characteristic
125	C₂×C₁₃	#544	1	1	yes	characteristic
126	C₂×C₁₃	#551	1	2	yes	—
127	C₂×C₁₃	#556	1	2	yes	—
128	C₂×Q₈	—	2	4	no	—
129	C₂×Q₈	—	2	4	no	—
130	C₂×Q₈	—	4	2	no	—
131	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
132	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
133	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
134	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
135	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
136	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
137	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
138	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
139	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
140	C₄⋊C₄	—	2	4	no	—
141	C₄⋊C₄	—	2	4	no	—
142	C₄⋊C₄	—	2	4	no	—
143	C₄⋊C₄	—	4	2	no	—
144	C₄²	—	2	4	no	—
145	C₄²	—	4	1	no	—
146	C₄²	—	4	1	no	—
147	C₄²	Q₈×C₁₃	1	4	yes	complemented
148	C₁₃	#2605	1	1	yes	characteristic, direct product factor, Sylow
149	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
150	Q₈	—	4	8	no	—
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	2	2	no	—
155	C₂×C₄	—	2	1	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	2	1	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	C₂×Q₈×C₁₃	1	2	yes	—
172	C₂×C₄	C₂×Q₈×C₁₃	1	2	yes	—
173	C₂×C₄	C₂×Q₈×C₁₃	1	2	yes	—
174	C₂×C₄	C₁₃×#41	1	4	yes	—
175	C₂×C₄	C₁₃×#41	1	4	yes	—
176	C₂²	C₂²×Q₈×C₁₃	1	1	yes	characteristic
177	C₂²	C₂×C₁₃×#41	1	2	yes	—
178	C₂²	C₂×C₁₃×#41	1	2	yes	—
179	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
180	C₂²	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
181	C₄	—	2	2	no	—
182	C₄	—	2	2	no	—
183	C₄	—	2	2	no	—
184	C₄	—	2	4	no	—
185	C₄	—	2	4	no	—
186	C₄	—	4	2	no	—
187	C₄	—	4	2	no	—
188	C₄	—	4	2	no	—
189	C₄	—	4	2	no	—
190	C₂	C₁₃×#533	1	1	yes	characteristic
191	C₂	C₁₃×#533	1	1	yes	characteristic
192	C₂	C₁₃×#544	1	1	yes	characteristic
193	C₂	C₁₃×#551	1	2	yes	—
194	C₂	C₁₃×#556	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
50. C₄²×C₁₃	Q₈	semidirect
51. #2605	C₁₃	direct (N × H)
147. C₄²	Q₈×C₁₃	semidirect
148. C₁₃	#2605	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×#400	2
C₁₃×#395	2
C₁₃×#391	2
C₁₃×#387	2
C₁₃×#383	2
C₄×C₁₃×C₄⋊C₄	2
C₁₃×#376	2
#2605	13

Subgroups — C13×#2605 #13111663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2605 #13111663