Subgroups — C₁₃×#2599 #13111657

Order 1664.

492 conjugacy classes of subgroups.

The subgroup lattice has 254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#397	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#395	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#393	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#388	C₂	1	2	yes	maximal
8	C₁₃×#387	C₂	1	2	yes	maximal, complemented
9	C₁₃×#387	C₂	1	2	yes	maximal, complemented
10	C₁₃×#385	C₂	1	2	yes	maximal
11	C₁₃×#383	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₄×Q₈×C₁₃	—	2	4	no	—
15	C₁₃×#117	—	2	4	no	—
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	1	yes	characteristic
19	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
28	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#95	C₂²	1	2	yes	—
30	C₁₃×#95	C₂²	1	2	yes	—
31	C₁₃×#95	C₂²	1	1	yes	characteristic
32	C₁₃×#95	C₂²	1	1	yes	characteristic
33	C₁₃×#95	C₂²	1	2	yes	—
34	C₁₃×#95	C₂²	1	2	yes	—
35	C₁₃×#95	C₂²	1	2	yes	—
36	C₁₃×#95	C₂²	1	2	yes	—
37	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
38	C₂×Q₈×C₁₃	—	2	2	no	—
39	C₂×Q₈×C₁₃	—	2	4	no	—
40	C₂²×C₄×C₁₃	—	2	2	no	—
41	C₂²×C₄×C₁₃	—	2	2	no	—
42	C₂²×C₄×C₁₃	—	2	2	no	—
43	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
44	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×C₄⋊C₄	—	2	2	no	—
54	C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₁₃×C₄⋊C₄	—	2	4	no	—
56	C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₁₃×C₄⋊C₄	—	2	4	no	—
58	C₁₃×C₄⋊C₄	—	2	4	no	—
59	C₁₃×C₂²⋊C₄	—	2	4	no	—
60	C₁₃×C₂²⋊C₄	—	2	2	no	—
61	C₁₃×C₂²⋊C₄	—	2	2	no	—
62	C₁₃×C₂²⋊C₄	—	2	4	no	—
63	C₄²×C₁₃	—	2	2	no	—
64	C₄²×C₁₃	—	2	4	no	—
65	C₄²×C₁₃	D₄	1	4	yes	—
66	#2599	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
67	C₂³×C₁₃	—	2	1	no	—
68	C₂³×C₁₃	—	2	2	no	—
69	C₂³×C₁₃	—	2	1	no	—
70	C₂³×C₁₃	—	2	2	no	—
71	C₂³×C₁₃	#41	1	2	yes	—
72	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
73	Q₈×C₁₃	—	2	8	no	—
74	C₂×C₄×C₁₃	—	2	8	no	—
75	C₂×C₄×C₁₃	—	2	2	no	—
76	C₂×C₄×C₁₃	—	2	1	no	—
77	C₂×C₄×C₁₃	—	2	1	no	—
78	C₂×C₄×C₁₃	—	2	1	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	2	no	—
83	C₂×C₄×C₁₃	—	2	1	no	—
84	C₂×C₄×C₁₃	—	2	1	no	—
85	C₂×C₄×C₁₃	—	2	2	no	—
86	C₂×C₄×C₁₃	—	2	2	no	—
87	C₂×C₄×C₁₃	—	2	2	no	—
88	C₂×C₄×C₁₃	—	2	2	no	—
89	C₂×C₄×C₁₃	—	2	2	no	—
90	C₂×C₄×C₁₃	—	2	2	no	—
91	C₂×C₄×C₁₃	—	2	2	no	—
92	C₂×C₄×C₁₃	—	2	2	no	—
93	C₂×C₄×C₁₃	—	2	2	no	—
94	C₂×C₄×C₁₃	—	2	2	no	—
95	C₂×C₄×C₁₃	—	2	2	no	—
96	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
97	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
98	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
99	C₂×C₄×C₁₃	#41	1	4	yes	—
100	C₂×C₄×C₁₃	#41	1	2	yes	—
101	C₂×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
102	C₂×#117	C₂×C₁₃	1	1	yes	characteristic
103	#398	C₂×C₁₃	1	1	yes	characteristic, complemented
104	#397	C₂×C₁₃	1	1	yes	characteristic
105	#395	C₂×C₁₃	1	1	yes	characteristic, complemented
106	#393	C₂×C₁₃	1	1	yes	characteristic
107	#388	C₂×C₁₃	1	2	yes	—
108	#387	C₂×C₁₃	1	2	yes	complemented
109	#387	C₂×C₁₃	1	2	yes	complemented
110	#385	C₂×C₁₃	1	2	yes	—
111	#383	C₂×C₁₃	1	1	yes	characteristic, complemented
112	C₂²×C₁₃	—	2	2	no	—
113	C₂²×C₁₃	—	2	4	no	—
114	C₂²×C₁₃	—	4	1	no	—
115	C₂²×C₁₃	—	4	1	no	—
116	C₂²×C₁₃	—	4	2	no	—
117	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
118	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
119	C₂²×C₁₃	C₂×#41	1	2	yes	—
120	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
121	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
122	C₄×C₁₃	—	2	2	no	—
123	C₄×C₁₃	—	2	2	no	—
124	C₄×C₁₃	—	2	2	no	—
125	C₄×C₁₃	—	2	4	no	—
126	C₄×C₁₃	—	2	2	no	—
127	C₄×C₁₃	—	4	1	no	—
128	C₄×C₁₃	—	4	2	no	—
129	C₄×C₁₃	—	4	1	no	—
130	C₄×C₁₃	—	4	2	no	—
131	C₄×C₁₃	—	4	2	no	—
132	C₂²×Q₈	C₂²×C₁₃	1	1	yes	characteristic
133	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic
134	C₄×Q₈	—	2	4	no	—
135	#117	—	2	4	no	—
136	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
137	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
138	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
139	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
140	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
141	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
142	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
143	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
144	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
145	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
146	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
147	C₂×C₄²	C₂²×C₁₃	1	2	yes	—
148	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
149	#95	C₂²×C₁₃	1	2	yes	—
150	#95	C₂²×C₁₃	1	2	yes	—
151	#95	C₂²×C₁₃	1	1	yes	characteristic
152	#95	C₂²×C₁₃	1	1	yes	characteristic
153	#95	C₂²×C₁₃	1	2	yes	—
154	#95	C₂²×C₁₃	1	2	yes	—
155	#95	C₂²×C₁₃	1	2	yes	—
156	#95	C₂²×C₁₃	1	2	yes	—
157	C₂×C₁₃	—	4	2	no	—
158	C₂×C₁₃	#525	1	1	yes	characteristic
159	C₂×C₁₃	#525	1	1	yes	characteristic
160	C₂×C₁₃	#536	1	1	yes	characteristic
161	C₂×C₁₃	#552	1	2	yes	—
162	C₂×C₁₃	#556	1	2	yes	—
163	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
164	C₂×Q₈	—	2	2	no	—
165	C₂×Q₈	—	2	4	no	—
166	C₂²×C₄	—	2	2	no	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
170	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
171	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
172	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
173	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
174	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
175	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
176	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
177	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
178	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	2	4	no	—
182	C₄⋊C₄	—	2	2	no	—
183	C₄⋊C₄	—	2	4	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₂²⋊C₄	—	2	4	no	—
186	C₂²⋊C₄	—	2	2	no	—
187	C₂²⋊C₄	—	2	2	no	—
188	C₂²⋊C₄	—	2	4	no	—
189	C₄²	—	2	2	no	—
190	C₄²	—	2	4	no	—
191	C₄²	D₄×C₁₃	1	4	yes	—
192	C₁₃	#2599	1	1	yes	characteristic, direct product factor, Sylow
193	C₂³	—	2	1	no	—
194	C₂³	—	2	2	no	—
195	C₂³	—	2	1	no	—
196	C₂³	—	2	2	no	—
197	C₂³	C₁₃×#41	1	2	yes	—
198	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
199	Q₈	—	2	8	no	—
200	C₂×C₄	—	2	8	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
223	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
224	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
225	C₂×C₄	C₁₃×#41	1	4	yes	—
226	C₂×C₄	C₁₃×#41	1	2	yes	—
227	C₂²	—	2	2	no	—
228	C₂²	—	2	4	no	—
229	C₂²	—	4	1	no	—
230	C₂²	—	4	1	no	—
231	C₂²	—	4	2	no	—
232	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
233	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
234	C₂²	C₂×C₁₃×#41	1	2	yes	—
235	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
236	C₂²	C₁₃×2₋¹⁺⁴	1	2	yes	—
237	C₄	—	2	2	no	—
238	C₄	—	2	2	no	—
239	C₄	—	2	2	no	—
240	C₄	—	2	4	no	—
241	C₄	—	2	2	no	—
242	C₄	—	4	1	no	—
243	C₄	—	4	2	no	—
244	C₄	—	4	1	no	—
245	C₄	—	4	2	no	—
246	C₄	—	4	2	no	—
247	C₂	—	4	2	no	—
248	C₂	C₁₃×#525	1	1	yes	characteristic
249	C₂	C₁₃×#525	1	1	yes	characteristic
250	C₂	C₁₃×#536	1	1	yes	characteristic
251	C₂	C₁₃×#552	1	2	yes	—
252	C₂	C₁₃×#556	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
1. C₂×C₄×Q₈×C₁₃	C₂	semidirect
3. C₁₃×#398	C₂	semidirect
5. C₁₃×#395	C₂	semidirect
8. C₁₃×#387	C₂	semidirect
9. C₁₃×#387	C₂	semidirect
11. C₁₃×#383	C₂	semidirect
66. #2599	C₁₃	direct (N × H)
101. C₂×C₄×Q₈	C₂×C₁₃	semidirect
103. #398	C₂×C₁₃	semidirect
105. #395	C₂×C₁₃	semidirect
108. #387	C₂×C₁₃	semidirect
109. #387	C₂×C₁₃	semidirect
111. #383	C₂×C₁₃	semidirect
192. C₁₃	#2599	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×C₄×Q₈×C₁₃	2
C₂×C₁₃×#117	2
C₁₃×#398	2
C₁₃×#397	2
C₁₃×#395	2
C₁₃×#393	2
C₁₃×#388	2
C₁₃×#387	2
C₁₃×#385	2
C₁₃×#383	2
#2599	13

Subgroups — C13×#2599 #13111657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2599 #13111657