Subgroups — C₁₃×#2625 #13111683

Order 1664.

464 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	C₂×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#400	C₂	1	2	yes	maximal, complemented
4	C₁₃×#398	C₂	1	2	yes	maximal, complemented
5	C₁₃×#397	C₂	1	4	yes	maximal
6	C₁₃×#391	C₂	1	2	yes	maximal, complemented
7	C₁₃×#389	C₂	1	2	yes	maximal, complemented
8	C₁₃×#380	C₂	1	1	yes	maximal, characteristic
9	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×C₂²⋊Q₈	—	2	4	no	—
12	C₁₃×#117	—	2	4	no	—
13	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
19	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
23	C₁₃×#95	C₂²	1	2	yes	—
24	C₁₃×#95	C₂²	1	4	yes	—
25	C₁₃×#95	C₂²	1	4	yes	—
26	C₁₃×#95	C₂²	1	4	yes	—
27	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
28	C₂×Q₈×C₁₃	—	2	2	no	—
29	C₂×Q₈×C₁₃	—	2	4	no	—
30	C₂²×C₄×C₁₃	—	2	4	no	—
31	C₂²×C₄×C₁₃	D₄	1	4	yes	—
32	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
33	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
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	1	yes	characteristic
38	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
39	C₁₃×C₄⋊C₄	—	2	2	no	—
40	C₁₃×C₄⋊C₄	—	2	2	no	—
41	C₁₃×C₄⋊C₄	—	2	2	no	—
42	C₁₃×C₄⋊C₄	—	2	4	no	—
43	C₁₃×C₄⋊C₄	—	2	4	no	—
44	C₁₃×C₄⋊C₄	—	4	4	no	—
45	C₁₃×C₂²⋊C₄	—	2	4	no	—
46	C₁₃×C₂²⋊C₄	—	2	4	no	—
47	C₁₃×C₂²⋊C₄	—	4	2	no	—
48	C₄²×C₁₃	—	2	4	no	—
49	#2625	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂³×C₁₃	—	2	2	no	—
51	C₂³×C₁₃	—	2	1	no	—
52	C₂³×C₁₃	—	2	2	no	—
53	C₂³×C₁₃	—	2	1	no	—
54	C₂³×C₁₃	C₂×D₄	1	2	yes	—
55	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
56	Q₈×C₁₃	—	4	4	no	—
57	C₂×C₄×C₁₃	—	2	2	no	—
58	C₂×C₄×C₁₃	—	2	8	no	—
59	C₂×C₄×C₁₃	—	2	2	no	—
60	C₂×C₄×C₁₃	—	2	2	no	—
61	C₂×C₄×C₁₃	—	2	2	no	—
62	C₂×C₄×C₁₃	—	2	2	no	—
63	C₂×C₄×C₁₃	—	2	4	no	—
64	C₂×C₄×C₁₃	—	2	4	no	—
65	C₂×C₄×C₁₃	—	2	4	no	—
66	C₂×C₄×C₁₃	—	2	2	no	—
67	C₂×C₄×C₁₃	—	2	2	no	—
68	C₂×C₄×C₁₃	—	2	4	no	—
69	C₂×C₄×C₁₃	—	2	2	no	—
70	C₂×C₄×C₁₃	—	2	2	no	—
71	C₂×C₄×C₁₃	—	2	4	no	—
72	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
73	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
74	C₂×C₄×C₁₃	#41	1	4	yes	—
75	C₂×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
76	C₂×#117	C₂×C₁₃	1	1	yes	characteristic
77	#400	C₂×C₁₃	1	2	yes	complemented
78	#398	C₂×C₁₃	1	2	yes	complemented
79	#397	C₂×C₁₃	1	4	yes	—
80	#391	C₂×C₁₃	1	2	yes	complemented
81	#389	C₂×C₁₃	1	2	yes	complemented
82	#380	C₂×C₁₃	1	1	yes	characteristic
83	C₂²×C₁₃	—	2	2	no	—
84	C₂²×C₁₃	—	2	2	no	—
85	C₂²×C₁₃	—	2	2	no	—
86	C₂²×C₁₃	—	4	2	no	—
87	C₂²×C₁₃	—	4	2	no	—
88	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
89	C₂²×C₁₃	C₂×#41	1	2	yes	—
90	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
91	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
92	C₂²×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
93	C₄×C₁₃	—	2	2	no	—
94	C₄×C₁₃	—	4	2	no	—
95	C₄×C₁₃	—	4	2	no	—
96	C₄×C₁₃	—	4	2	no	—
97	C₄×C₁₃	—	4	2	no	—
98	C₄×C₁₃	—	4	4	no	—
99	C₄×C₁₃	#123	1	4	yes	—
100	C₂²×Q₈	C₂²×C₁₃	1	1	yes	characteristic
101	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic
102	C₂²⋊Q₈	—	2	4	no	—
103	#117	—	2	4	no	—
104	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
105	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
106	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
107	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
108	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
109	C₂×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
110	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
111	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
112	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
113	C₂×C₄²	C₂²×C₁₃	1	2	yes	—
114	#95	C₂²×C₁₃	1	2	yes	—
115	#95	C₂²×C₁₃	1	4	yes	—
116	#95	C₂²×C₁₃	1	4	yes	—
117	#95	C₂²×C₁₃	1	4	yes	—
118	C₂×C₁₃	—	4	2	no	—
119	C₂×C₁₃	C₂×#123	1	1	yes	characteristic
120	C₂×C₁₃	#536	1	1	yes	characteristic
121	C₂×C₁₃	#537	1	1	yes	characteristic
122	C₂×C₁₃	#541	1	2	yes	—
123	C₂×C₁₃	#542	1	2	yes	—
124	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
125	C₂×Q₈	—	2	2	no	—
126	C₂×Q₈	—	2	4	no	—
127	C₂²×C₄	—	2	4	no	—
128	C₂²×C₄	D₄×C₁₃	1	4	yes	—
129	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
130	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
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	1	yes	characteristic
135	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
136	C₄⋊C₄	—	2	2	no	—
137	C₄⋊C₄	—	2	2	no	—
138	C₄⋊C₄	—	2	2	no	—
139	C₄⋊C₄	—	2	4	no	—
140	C₄⋊C₄	—	2	4	no	—
141	C₄⋊C₄	—	4	4	no	—
142	C₂²⋊C₄	—	2	4	no	—
143	C₂²⋊C₄	—	2	4	no	—
144	C₂²⋊C₄	—	4	2	no	—
145	C₄²	—	2	4	no	—
146	C₁₃	#2625	1	1	yes	characteristic, direct product factor, Sylow
147	C₂³	—	2	2	no	—
148	C₂³	—	2	1	no	—
149	C₂³	—	2	2	no	—
150	C₂³	—	2	1	no	—
151	C₂³	C₂×D₄×C₁₃	1	2	yes	—
152	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
153	Q₈	—	4	4	no	—
154	C₂×C₄	—	2	2	no	—
155	C₂×C₄	—	2	8	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	4	no	—
161	C₂×C₄	—	2	4	no	—
162	C₂×C₄	—	2	4	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	4	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	4	no	—
169	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
170	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
171	C₂×C₄	C₁₃×#41	1	4	yes	—
172	C₂²	—	2	2	no	—
173	C₂²	—	2	2	no	—
174	C₂²	—	2	2	no	—
175	C₂²	—	4	2	no	—
176	C₂²	—	4	2	no	—
177	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
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	2	yes	—
181	C₂²	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
182	C₄	—	2	2	no	—
183	C₄	—	4	2	no	—
184	C₄	—	4	2	no	—
185	C₄	—	4	2	no	—
186	C₄	—	4	2	no	—
187	C₄	—	4	4	no	—
188	C₄	C₁₃×#123	1	4	yes	—
189	C₂	—	4	2	no	—
190	C₂	C₂×C₁₃×#123	1	1	yes	characteristic
191	C₂	C₁₃×#536	1	1	yes	characteristic
192	C₂	C₁₃×#537	1	1	yes	characteristic
193	C₂	C₁₃×#541	1	2	yes	—
194	C₂	C₁₃×#542	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂³
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
3. C₁₃×#400	C₂	semidirect
4. C₁₃×#398	C₂	semidirect
6. C₁₃×#391	C₂	semidirect
7. C₁₃×#389	C₂	semidirect
49. #2625	C₁₃	direct (N × H)
77. #400	C₂×C₁₃	semidirect
78. #398	C₂×C₁₃	semidirect
80. #391	C₂×C₁₃	semidirect
81. #389	C₂×C₁₃	semidirect
146. C₁₃	#2625	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×C₂²⋊Q₈	2
C₂×C₁₃×#117	2
C₁₃×#400	2
C₁₃×#398	2
C₁₃×#397	2
C₁₃×#391	2
C₁₃×#389	2
C₁₃×#380	2
#2625	13

Subgroups — C13×#2625 #13111683

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2625 #13111683