Subgroups — C₁₃×#7720 #15694059

Order 3328.

388 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2859	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1839	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1831	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1271	C₂	1	4	yes	maximal
5	C₂×C₁₃×#125	—	2	1	no	—
6	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
7	C₁₃×#389	—	2	1	no	—
8	C₁₃×#389	—	2	1	no	—
9	C₁₃×#389	C₄	1	2	yes	—
10	C₁₃×#389	C₂²	1	2	yes	—
11	C₁₃×#384	C₄	1	1	yes	characteristic
12	C₁₃×#384	C₄	1	1	yes	characteristic
13	C₁₃×#382	—	2	1	no	—
14	C₄³×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#336	—	2	1	no	—
16	C₁₃×#336	—	2	1	no	—
17	C₁₃×#336	—	2	1	no	—
18	C₁₃×#336	C₂²	1	2	yes	—
19	C₁₃×#336	C₂²	1	2	yes	—
20	C₂²×C₈×C₁₃	—	2	2	no	—
21	C₂²×C₈×C₁₃	—	2	2	no	—
22	C₁₃×#125	—	4	4	no	—
23	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
24	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
25	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
28	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
29	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
30	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
38	C₁₃×C₄⋊C₈	—	4	2	no	—
39	C₁₃×#95	—	2	2	no	—
40	C₁₃×#95	—	2	2	no	—
41	#7720	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₄×C₁₃	—	2	2	no	—
43	C₂²×C₄×C₁₃	—	2	2	no	—
44	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
51	C₂×C₈×C₁₃	—	4	2	no	—
52	C₂×C₈×C₁₃	—	4	2	no	—
53	C₂×C₈×C₁₃	—	4	2	no	—
54	C₂×C₈×C₁₃	—	4	2	no	—
55	C₂×C₈×C₁₃	—	4	2	no	—
56	C₂×C₈×C₁₃	—	4	2	no	—
57	C₁₃×C₄⋊C₄	—	2	4	no	—
58	C₁₃×C₄⋊C₄	—	4	2	no	—
59	C₁₃×C₄⋊C₄	—	4	2	no	—
60	C₁₃×C₄⋊C₄	—	4	2	no	—
61	C₁₃×C₄⋊C₄	—	4	2	no	—
62	C₁₃×C₄⋊C₄	—	4	2	no	—
63	C₁₃×C₄⋊C₄	—	4	4	no	—
64	C₁₃×C₄⋊C₄	—	4	4	no	—
65	C₄²×C₁₃	—	2	2	no	—
66	C₄²×C₁₃	—	2	2	no	—
67	C₄²×C₁₃	—	2	2	no	—
68	C₄²×C₁₃	—	4	1	no	—
69	C₄²×C₁₃	—	4	1	no	—
70	C₄²×C₁₃	—	4	1	no	—
71	C₄²×C₁₃	SD₁₆	1	2	yes	—
72	C₄²×C₁₃	Q₁₆	1	2	yes	—
73	#2859	C₂×C₁₃	1	1	yes	characteristic
74	#1839	C₂×C₁₃	1	1	yes	characteristic
75	#1831	C₂×C₁₃	1	1	yes	characteristic
76	#1271	C₂×C₁₃	1	4	yes	—
77	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₄×C₁₃	—	2	1	no	—
79	C₂×C₄×C₁₃	—	2	1	no	—
80	C₂×C₄×C₁₃	—	2	1	no	—
81	C₂×C₄×C₁₃	—	2	1	no	—
82	C₂×C₄×C₁₃	—	2	1	no	—
83	C₂×C₄×C₁₃	—	2	1	no	—
84	C₂×C₄×C₁₃	—	2	1	no	—
85	C₂×C₄×C₁₃	—	2	1	no	—
86	C₂×C₄×C₁₃	—	2	1	no	—
87	C₂×C₄×C₁₃	—	2	1	no	—
88	C₂×C₄×C₁₃	—	2	1	no	—
89	C₂×C₄×C₁₃	—	2	1	no	—
90	C₂×C₄×C₁₃	—	2	1	no	—
91	C₂×C₄×C₁₃	—	2	1	no	—
92	C₂×C₄×C₁₃	—	2	1	no	—
93	C₂×C₄×C₁₃	—	4	2	no	—
94	C₂×C₄×C₁₃	—	4	2	no	—
95	C₂×C₄×C₁₃	—	4	2	no	—
96	C₂×C₄×C₁₃	—	4	2	no	—
97	C₂×C₄×C₁₃	—	4	2	no	—
98	C₂×C₄×C₁₃	—	4	2	no	—
99	C₂×C₄×C₁₃	#101	1	2	yes	—
100	C₂×C₄×C₁₃	#103	1	2	yes	—
101	C₂×C₄×C₁₃	#103	1	2	yes	—
102	C₂×C₄×C₁₃	#131	1	2	yes	—
103	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
104	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
105	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
106	C₈×C₁₃	—	8	2	no	—
107	C₈×C₁₃	—	8	2	no	—
108	C₂×#125	—	2	1	no	—
109	C₂×C₄⋊C₈	—	2	1	no	—
110	#389	—	2	1	no	—
111	#389	—	2	1	no	—
112	#389	C₄×C₁₃	1	2	yes	—
113	#389	C₂²×C₁₃	1	2	yes	—
114	#384	C₄×C₁₃	1	1	yes	characteristic
115	#384	C₄×C₁₃	1	1	yes	characteristic
116	#382	—	2	1	no	—
117	C₄³	C₂²×C₁₃	1	1	yes	characteristic
118	#336	—	2	1	no	—
119	#336	—	2	1	no	—
120	#336	—	2	1	no	—
121	#336	C₂²×C₁₃	1	2	yes	—
122	#336	C₂²×C₁₃	1	2	yes	—
123	C₂²×C₁₃	#408	1	1	yes	characteristic
124	C₂²×C₁₃	#410	1	1	yes	characteristic
125	C₂²×C₁₃	C₂×#101	1	1	yes	characteristic
126	C₂²×C₁₃	C₂×#103	1	1	yes	characteristic
127	C₂²×C₁₃	#418	1	1	yes	characteristic
128	C₂²×C₁₃	#421	1	1	yes	characteristic
129	C₂²×C₁₃	#421	1	1	yes	characteristic
130	C₄×C₁₃	—	2	2	no	—
131	C₄×C₁₃	—	2	2	no	—
132	C₄×C₁₃	—	2	2	no	—
133	C₄×C₁₃	—	2	2	no	—
134	C₄×C₁₃	—	2	1	no	—
135	C₄×C₁₃	—	2	1	no	—
136	C₄×C₁₃	—	2	2	no	—
137	C₄×C₁₃	—	4	1	no	—
138	C₄×C₁₃	—	8	2	no	—
139	C₄×C₁₃	—	8	2	no	—
140	C₂²×C₈	—	2	2	no	—
141	C₂²×C₈	—	2	2	no	—
142	#125	—	4	4	no	—
143	C₂×C₄⋊C₄	—	2	1	no	—
144	C₂×C₄⋊C₄	—	2	1	no	—
145	C₂×C₄⋊C₄	—	2	2	no	—
146	C₂×C₄⋊C₄	—	2	1	no	—
147	C₂×C₄⋊C₄	—	2	1	no	—
148	C₂×C₄⋊C₄	—	2	2	no	—
149	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
150	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
151	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
152	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
153	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
154	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
155	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
156	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
157	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
158	C₄⋊C₈	—	4	2	no	—
159	#95	—	2	2	no	—
160	#95	—	2	2	no	—
161	C₂×C₁₃	#1470	1	1	yes	characteristic
162	C₂×C₁₃	#1481	1	1	yes	characteristic
163	C₂×C₁₃	#1496	1	1	yes	characteristic
164	C₂×C₁₃	#1514	1	1	yes	characteristic
165	C₂×C₁₃	#1518	1	1	yes	characteristic
166	C₂×C₁₃	#1534	1	1	yes	characteristic
167	C₂×C₁₃	#1549	1	1	yes	characteristic
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
172	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
173	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
174	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
175	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
176	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
177	C₂×C₈	—	4	2	no	—
178	C₂×C₈	—	4	2	no	—
179	C₂×C₈	—	4	2	no	—
180	C₂×C₈	—	4	2	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	4	2	no	—
183	C₄⋊C₄	—	2	4	no	—
184	C₄⋊C₄	—	4	2	no	—
185	C₄⋊C₄	—	4	2	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₄⋊C₄	—	4	4	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄⋊C₄	—	4	2	no	—
190	C₄⋊C₄	—	4	4	no	—
191	C₄²	—	2	2	no	—
192	C₄²	—	2	2	no	—
193	C₄²	—	2	2	no	—
194	C₄²	—	4	1	no	—
195	C₄²	—	4	1	no	—
196	C₄²	—	4	1	no	—
197	C₄²	C₁₃×SD₁₆	1	2	yes	—
198	C₄²	C₁₃×Q₁₆	1	2	yes	—
199	C₁₃	#7720	1	1	yes	characteristic, direct product factor, Sylow
200	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₄	—	2	1	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	1	no	—
207	C₂×C₄	—	2	1	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	4	2	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	C₁₃×#101	1	2	yes	—
223	C₂×C₄	C₁₃×#103	1	2	yes	—
224	C₂×C₄	C₁₃×#103	1	2	yes	—
225	C₂×C₄	C₁₃×#131	1	2	yes	—
226	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
227	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
228	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
229	C₈	—	8	2	no	—
230	C₈	—	8	2	no	—
231	C₂²	C₁₃×#408	1	1	yes	characteristic
232	C₂²	C₁₃×#410	1	1	yes	characteristic
233	C₂²	C₂×C₁₃×#101	1	1	yes	characteristic
234	C₂²	C₂×C₁₃×#103	1	1	yes	characteristic
235	C₂²	C₁₃×#418	1	1	yes	characteristic
236	C₂²	C₁₃×#421	1	1	yes	characteristic
237	C₂²	C₁₃×#421	1	1	yes	characteristic
238	C₄	—	2	2	no	—
239	C₄	—	2	2	no	—
240	C₄	—	2	2	no	—
241	C₄	—	2	1	no	—
242	C₄	—	2	1	no	—
243	C₄	—	2	2	no	—
244	C₄	—	2	2	no	—
245	C₄	—	4	1	no	—
246	C₄	—	8	2	no	—
247	C₄	—	8	2	no	—
248	C₂	C₁₃×#1470	1	1	yes	characteristic
249	C₂	C₁₃×#1481	1	1	yes	characteristic
250	C₂	C₁₃×#1496	1	1	yes	characteristic
251	C₂	C₁₃×#1514	1	1	yes	characteristic
252	C₂	C₁₃×#1518	1	1	yes	characteristic
253	C₂	C₁₃×#1534	1	1	yes	characteristic
254	C₂	C₁₃×#1549	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
41. #7720	C₁₃	direct (N × H)
199. C₁₃	#7720	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×#2859	2
C₁₃×#1839	2
C₁₃×#1831	2
C₁₃×#1271	2
#7720	13

Subgroups — C13×#7720 #15694059

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#7720 #15694059