Subgroups — C₁₃×#2507 #13111565

Order 1664.

396 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#398	C₂	1	2	yes	maximal
2	C₁₃×#398	C₂	1	2	yes	maximal
3	C₁₃×#389	C₂	1	2	yes	maximal
4	C₁₃×#389	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#389	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#389	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#389	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#387	C₂	1	2	yes	maximal
9	C₁₃×#384	C₂	1	1	yes	maximal, characteristic
10	C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
18	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
28	C₁₃×#95	C₂²	1	1	yes	characteristic
29	C₁₃×#95	C₂²	1	1	yes	characteristic
30	C₁₃×#95	C₂²	1	2	yes	—
31	C₁₃×#95	C₂²	1	2	yes	—
32	C₁₃×#95	C₂²	1	2	yes	—
33	C₁₃×#95	C₂²	1	2	yes	—
34	C₁₃×#95	C₂²	1	2	yes	—
35	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
36	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
37	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
38	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
39	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
40	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
44	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₁₃×C₄⋊C₄	—	2	2	no	—
47	C₁₃×C₄⋊C₄	—	2	4	no	—
48	C₁₃×C₄⋊C₄	—	2	2	no	—
49	C₁₃×C₄⋊C₄	—	2	2	no	—
50	C₁₃×C₄⋊C₄	—	2	2	no	—
51	C₁₃×C₄⋊C₄	—	4	2	no	—
52	C₁₃×C₄⋊C₄	—	4	2	no	—
53	C₁₃×C₄⋊C₄	—	4	2	no	—
54	C₁₃×C₄⋊C₄	—	4	2	no	—
55	C₁₃×C₄⋊C₄	—	4	2	no	—
56	C₁₃×C₄⋊C₄	Q₈	1	4	yes	—
57	C₁₃×C₄⋊C₄	Q₈	1	4	yes	—
58	C₄²×C₁₃	—	2	2	no	—
59	C₄²×C₁₃	—	2	2	no	—
60	C₄²×C₁₃	—	2	2	no	—
61	C₄²×C₁₃	—	4	2	no	—
62	#2507	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
64	C₂×C₄×C₁₃	—	2	1	no	—
65	C₂×C₄×C₁₃	—	2	1	no	—
66	C₂×C₄×C₁₃	—	2	1	no	—
67	C₂×C₄×C₁₃	—	2	1	no	—
68	C₂×C₄×C₁₃	—	2	1	no	—
69	C₂×C₄×C₁₃	—	2	2	no	—
70	C₂×C₄×C₁₃	—	2	1	no	—
71	C₂×C₄×C₁₃	—	2	2	no	—
72	C₂×C₄×C₁₃	—	2	1	no	—
73	C₂×C₄×C₁₃	—	2	1	no	—
74	C₂×C₄×C₁₃	—	2	1	no	—
75	C₂×C₄×C₁₃	—	2	1	no	—
76	C₂×C₄×C₁₃	—	2	2	no	—
77	C₂×C₄×C₁₃	—	2	2	no	—
78	C₂×C₄×C₁₃	—	2	2	no	—
79	C₂×C₄×C₁₃	—	2	1	no	—
80	C₂×C₄×C₁₃	—	2	2	no	—
81	C₂×C₄×C₁₃	—	2	2	no	—
82	C₂×C₄×C₁₃	—	2	1	no	—
83	C₂×C₄×C₁₃	—	2	2	no	—
84	C₂×C₄×C₁₃	—	2	2	no	—
85	C₂×C₄×C₁₃	—	2	1	no	—
86	C₂×C₄×C₁₃	—	2	2	no	—
87	C₂×C₄×C₁₃	—	2	1	no	—
88	C₂×C₄×C₁₃	—	2	2	no	—
89	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
90	C₂×C₄×C₁₃	C₂×Q₈	1	4	yes	—
91	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
92	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
93	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
94	C₂×C₄×C₁₃	#41	1	2	yes	—
95	C₂×C₄×C₁₃	#41	1	2	yes	—
96	C₂×C₄×C₁₃	#41	1	2	yes	—
97	#398	C₂×C₁₃	1	2	yes	—
98	#398	C₂×C₁₃	1	2	yes	—
99	#389	C₂×C₁₃	1	2	yes	—
100	#389	C₂×C₁₃	1	1	yes	characteristic
101	#389	C₂×C₁₃	1	1	yes	characteristic
102	#389	C₂×C₁₃	1	1	yes	characteristic
103	#389	C₂×C₁₃	1	1	yes	characteristic
104	#387	C₂×C₁₃	1	2	yes	—
105	#384	C₂×C₁₃	1	1	yes	characteristic
106	C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
107	C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
108	C₂²×C₁₃	C₂²×Q₈	1	1	yes	characteristic
109	C₂²×C₁₃	C₂²×Q₈	1	1	yes	characteristic
110	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
111	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
112	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
113	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
114	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
115	C₄×C₁₃	—	2	2	no	—
116	C₄×C₁₃	—	2	2	no	—
117	C₄×C₁₃	—	2	2	no	—
118	C₄×C₁₃	—	2	2	no	—
119	C₄×C₁₃	—	2	4	no	—
120	C₄×C₁₃	—	4	1	no	—
121	C₄×C₁₃	—	4	2	no	—
122	C₄×C₁₃	—	4	2	no	—
123	C₄×C₁₃	—	4	1	no	—
124	C₄×C₁₃	—	4	2	no	—
125	C₄×C₁₃	#125	1	4	yes	—
126	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
127	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
128	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
129	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
130	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
131	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
132	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
133	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
134	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
135	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
136	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
137	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
138	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
139	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
140	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
141	C₂×C₄²	C₂²×C₁₃	1	2	yes	—
142	#95	C₂²×C₁₃	1	1	yes	characteristic
143	#95	C₂²×C₁₃	1	1	yes	characteristic
144	#95	C₂²×C₁₃	1	2	yes	—
145	#95	C₂²×C₁₃	1	2	yes	—
146	#95	C₂²×C₁₃	1	2	yes	—
147	#95	C₂²×C₁₃	1	2	yes	—
148	#95	C₂²×C₁₃	1	2	yes	—
149	C₂×C₁₃	C₂×#125	1	1	yes	characteristic
150	C₂×C₁₃	#533	1	1	yes	characteristic
151	C₂×C₁₃	#540	1	1	yes	characteristic
152	C₂×C₁₃	#553	1	1	yes	characteristic
153	C₂×C₁₃	#554	1	1	yes	characteristic
154	C₂×C₁₃	#554	1	1	yes	characteristic
155	C₂×C₁₃	Q₈²	1	1	yes	characteristic
156	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
157	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
158	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
159	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
160	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
161	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
162	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
163	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
164	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
165	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
166	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
167	C₄⋊C₄	—	2	2	no	—
168	C₄⋊C₄	—	2	4	no	—
169	C₄⋊C₄	—	2	2	no	—
170	C₄⋊C₄	—	2	2	no	—
171	C₄⋊C₄	—	2	2	no	—
172	C₄⋊C₄	—	4	2	no	—
173	C₄⋊C₄	—	4	2	no	—
174	C₄⋊C₄	—	4	2	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₄⋊C₄	Q₈×C₁₃	1	4	yes	—
178	C₄⋊C₄	Q₈×C₁₃	1	4	yes	—
179	C₄²	—	2	2	no	—
180	C₄²	—	2	2	no	—
181	C₄²	—	2	2	no	—
182	C₄²	—	4	2	no	—
183	C₁₃	#2507	1	1	yes	characteristic, direct product factor, Sylow
184	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	—	2	1	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	1	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	C₂×Q₈×C₁₃	1	2	yes	—
211	C₂×C₄	C₂×Q₈×C₁₃	1	4	yes	—
212	C₂×C₄	C₂×Q₈×C₁₃	1	2	yes	—
213	C₂×C₄	C₂×Q₈×C₁₃	1	2	yes	—
214	C₂×C₄	C₂×Q₈×C₁₃	1	2	yes	—
215	C₂×C₄	C₁₃×#41	1	2	yes	—
216	C₂×C₄	C₁₃×#41	1	2	yes	—
217	C₂×C₄	C₁₃×#41	1	2	yes	—
218	C₂²	C₂²×Q₈×C₁₃	1	1	yes	characteristic
219	C₂²	C₂²×Q₈×C₁₃	1	1	yes	characteristic
220	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
221	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
222	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
223	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
224	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
225	C₄	—	2	2	no	—
226	C₄	—	2	2	no	—
227	C₄	—	2	2	no	—
228	C₄	—	2	2	no	—
229	C₄	—	2	4	no	—
230	C₄	—	4	1	no	—
231	C₄	—	4	2	no	—
232	C₄	—	4	2	no	—
233	C₄	—	4	1	no	—
234	C₄	—	4	2	no	—
235	C₄	C₁₃×#125	1	4	yes	—
236	C₂	C₂×C₁₃×#125	1	1	yes	characteristic
237	C₂	C₁₃×#533	1	1	yes	characteristic
238	C₂	C₁₃×#540	1	1	yes	characteristic
239	C₂	C₁₃×#553	1	1	yes	characteristic
240	C₂	C₁₃×#554	1	1	yes	characteristic
241	C₂	C₁₃×#554	1	1	yes	characteristic
242	C₂	Q₈²×C₁₃	1	1	yes	characteristic

	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
62. #2507	C₁₃	direct (N × H)
183. C₁₃	#2507	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×#398	2
C₁₃×#389	2
C₁₃×#387	2
C₁₃×#384	2
C₄×C₁₃×C₄⋊C₄	2
#2507	13

Subgroups — C13×#2507 #13111565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2507 #13111565