Subgroups — C₁₃×#7723 #15694062

Order 3328.

388 conjugacy classes of subgroups.

The subgroup lattice has 260 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	2	no	—
23	C₁₃×#125	—	4	2	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	1	no	—
28	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
30	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
31	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
32	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₃	C₂×C₄	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	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
39	C₁₃×C₄⋊C₈	—	4	2	no	—
40	C₁₃×#95	—	2	2	no	—
41	C₁₃×#95	—	2	2	no	—
42	#7723	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₄×C₁₃	—	2	2	no	—
44	C₂²×C₄×C₁₃	—	2	2	no	—
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	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₂×C₈×C₁₃	—	4	2	no	—
58	C₁₃×C₄⋊C₄	—	2	4	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	2	no	—
64	C₁₃×C₄⋊C₄	—	4	4	no	—
65	C₁₃×C₄⋊C₄	—	4	2	no	—
66	C₁₃×C₄⋊C₄	—	4	2	no	—
67	C₄²×C₁₃	—	2	2	no	—
68	C₄²×C₁₃	—	2	2	no	—
69	C₄²×C₁₃	—	2	2	no	—
70	C₄²×C₁₃	—	4	1	no	—
71	C₄²×C₁₃	—	4	1	no	—
72	C₄²×C₁₃	—	4	1	no	—
73	C₄²×C₁₃	D₈	1	2	yes	—
74	C₄²×C₁₃	SD₁₆	1	2	yes	—
75	#2859	C₂×C₁₃	1	1	yes	characteristic
76	#1839	C₂×C₁₃	1	1	yes	characteristic
77	#1831	C₂×C₁₃	1	1	yes	characteristic
78	#1271	C₂×C₁₃	1	4	yes	—
79	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	—	2	1	no	—
94	C₂×C₄×C₁₃	—	2	1	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	—	4	2	no	—
100	C₂×C₄×C₁₃	—	4	2	no	—
101	C₂×C₄×C₁₃	#101	1	2	yes	—
102	C₂×C₄×C₁₃	#102	1	2	yes	—
103	C₂×C₄×C₁₃	#102	1	2	yes	—
104	C₂×C₄×C₁₃	#131	1	2	yes	—
105	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
106	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
107	C₂×C₄×C₁₃	#137	1	2	yes	—
108	C₈×C₁₃	—	8	2	no	—
109	C₈×C₁₃	—	8	2	no	—
110	C₂×#125	—	2	1	no	—
111	C₂×C₄⋊C₈	—	2	1	no	—
112	#389	—	2	1	no	—
113	#389	—	2	1	no	—
114	#389	C₄×C₁₃	1	2	yes	—
115	#389	C₂²×C₁₃	1	2	yes	—
116	#384	C₄×C₁₃	1	1	yes	characteristic
117	#384	C₄×C₁₃	1	1	yes	characteristic
118	#382	—	2	1	no	—
119	C₄³	C₂²×C₁₃	1	1	yes	characteristic
120	#336	—	2	1	no	—
121	#336	—	2	1	no	—
122	#336	—	2	1	no	—
123	#336	C₂²×C₁₃	1	2	yes	—
124	#336	C₂²×C₁₃	1	2	yes	—
125	C₂²×C₁₃	#408	1	1	yes	characteristic
126	C₂²×C₁₃	#410	1	1	yes	characteristic
127	C₂²×C₁₃	C₂×#101	1	1	yes	characteristic
128	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
129	C₂²×C₁₃	#419	1	1	yes	characteristic
130	C₂²×C₁₃	#421	1	1	yes	characteristic
131	C₂²×C₁₃	#421	1	1	yes	characteristic
132	C₄×C₁₃	—	2	2	no	—
133	C₄×C₁₃	—	2	2	no	—
134	C₄×C₁₃	—	2	2	no	—
135	C₄×C₁₃	—	2	2	no	—
136	C₄×C₁₃	—	2	1	no	—
137	C₄×C₁₃	—	2	1	no	—
138	C₄×C₁₃	—	2	2	no	—
139	C₄×C₁₃	—	4	1	no	—
140	C₄×C₁₃	—	8	2	no	—
141	C₄×C₁₃	—	8	2	no	—
142	C₂²×C₈	—	2	2	no	—
143	C₂²×C₈	—	2	2	no	—
144	#125	—	4	2	no	—
145	#125	—	4	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	—	2	1	no	—
150	C₂×C₄⋊C₄	—	2	1	no	—
151	C₂×C₄⋊C₄	—	2	2	no	—
152	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
153	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
154	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
155	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
156	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
157	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
158	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
159	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
160	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
161	C₄⋊C₈	—	4	2	no	—
162	#95	—	2	2	no	—
163	#95	—	2	2	no	—
164	C₂×C₁₃	#1470	1	1	yes	characteristic
165	C₂×C₁₃	#1480	1	1	yes	characteristic
166	C₂×C₁₃	#1497	1	1	yes	characteristic
167	C₂×C₁₃	#1515	1	1	yes	characteristic
168	C₂×C₁₃	#1517	1	1	yes	characteristic
169	C₂×C₁₃	#1534	1	1	yes	characteristic
170	C₂×C₁₃	#1546	1	1	yes	characteristic
171	C₂²×C₄	—	2	2	no	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
174	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
175	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
176	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
177	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
178	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
179	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
180	C₂×C₈	—	4	2	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	4	2	no	—
183	C₂×C₈	—	4	2	no	—
184	C₂×C₈	—	4	2	no	—
185	C₂×C₈	—	4	2	no	—
186	C₄⋊C₄	—	2	4	no	—
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄⋊C₄	—	4	2	no	—
190	C₄⋊C₄	—	4	2	no	—
191	C₄⋊C₄	—	4	2	no	—
192	C₄⋊C₄	—	4	4	no	—
193	C₄⋊C₄	—	4	2	no	—
194	C₄⋊C₄	—	4	2	no	—
195	C₄²	—	2	2	no	—
196	C₄²	—	2	2	no	—
197	C₄²	—	2	2	no	—
198	C₄²	—	4	1	no	—
199	C₄²	—	4	1	no	—
200	C₄²	—	4	1	no	—
201	C₄²	C₁₃×D₈	1	2	yes	—
202	C₄²	C₁₃×SD₁₆	1	2	yes	—
203	C₁₃	#7723	1	1	yes	characteristic, direct product factor, Sylow
204	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
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	—	2	1	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	4	2	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	C₁₃×#101	1	2	yes	—
227	C₂×C₄	C₁₃×#102	1	2	yes	—
228	C₂×C₄	C₁₃×#102	1	2	yes	—
229	C₂×C₄	C₁₃×#131	1	2	yes	—
230	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
231	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
232	C₂×C₄	C₁₃×#137	1	2	yes	—
233	C₈	—	8	2	no	—
234	C₈	—	8	2	no	—
235	C₂²	C₁₃×#408	1	1	yes	characteristic
236	C₂²	C₁₃×#410	1	1	yes	characteristic
237	C₂²	C₂×C₁₃×#101	1	1	yes	characteristic
238	C₂²	C₂×C₁₃×#102	1	1	yes	characteristic
239	C₂²	C₁₃×#419	1	1	yes	characteristic
240	C₂²	C₁₃×#421	1	1	yes	characteristic
241	C₂²	C₁₃×#421	1	1	yes	characteristic
242	C₄	—	2	2	no	—
243	C₄	—	2	2	no	—
244	C₄	—	2	2	no	—
245	C₄	—	2	1	no	—
246	C₄	—	2	1	no	—
247	C₄	—	2	2	no	—
248	C₄	—	2	2	no	—
249	C₄	—	4	1	no	—
250	C₄	—	8	2	no	—
251	C₄	—	8	2	no	—
252	C₂	C₁₃×#1470	1	1	yes	characteristic
253	C₂	C₁₃×#1480	1	1	yes	characteristic
254	C₂	C₁₃×#1497	1	1	yes	characteristic
255	C₂	C₁₃×#1515	1	1	yes	characteristic
256	C₂	C₁₃×#1517	1	1	yes	characteristic
257	C₂	C₁₃×#1534	1	1	yes	characteristic
258	C₂	C₁₃×#1546	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
42. #7723	C₁₃	direct (N × H)
203. C₁₃	#7723	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
#7723	13

Subgroups — C13×#7723 #15694062

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#7723 #15694062