Subgroups — C₁₃×#10543 #15696882

Order 3328.

422 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1987	C₂	1	2	yes	maximal
3	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#333	C₂	1	2	yes	maximal
5	C₁₃×#1277	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
7	C₁₃×#500	—	2	4	no	—
8	C₂×C₁₃×#107	—	2	1	no	—
9	C₂×C₁₃×#107	—	2	1	no	—
10	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
11	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
12	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₁₃×#340	—	2	2	no	—
16	C₁₃×#340	—	2	2	no	—
17	C₁₃×#336	—	2	1	no	—
18	C₁₃×#333	—	2	4	no	—
19	C₂²×Q₈×C₁₃	—	2	2	no	—
20	C₂²×C₈×C₁₃	—	2	1	no	—
21	C₂²×C₈×C₁₃	—	2	2	no	—
22	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
24	C₁₃×C₄⋊Q₈	—	2	2	no	—
25	C₁₃×C₄⋊Q₈	—	2	2	no	—
26	C₁₃×C₄⋊Q₈	—	2	2	no	—
27	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
28	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
30	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
31	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₃	—	2	1	no	—
33	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
34	C₁₃×#107	—	2	4	no	—
35	C₁₃×#107	—	2	4	no	—
36	C₁₃×C₄⋊C₈	—	2	2	no	—
37	C₁₃×C₄⋊C₈	—	2	2	no	—
38	C₁₃×C₄⋊C₈	—	2	2	no	—
39	C₁₃×C₄⋊C₈	—	4	2	no	—
40	C₄×C₈×C₁₃	—	2	2	no	—
41	C₁₃×#95	—	2	1	no	—
42	#10543	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂×Q₈×C₁₃	—	2	4	no	—
44	C₂×Q₈×C₁₃	—	4	2	no	—
45	C₂×Q₈×C₁₃	—	8	2	no	—
46	C₂×Q₈×C₁₃	—	8	2	no	—
47	C₂²×C₄×C₁₃	—	2	1	no	—
48	C₂²×C₄×C₁₃	—	2	1	no	—
49	C₂²×C₄×C₁₃	—	4	2	no	—
50	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
53	C₂×C₈×C₁₃	—	2	1	no	—
54	C₂×C₈×C₁₃	—	2	1	no	—
55	C₂×C₈×C₁₃	—	2	1	no	—
56	C₂×C₈×C₁₃	—	2	1	no	—
57	C₂×C₈×C₁₃	—	4	1	no	—
58	C₂×C₈×C₁₃	—	4	2	no	—
59	C₂×C₈×C₁₃	—	4	1	no	—
60	C₂×C₈×C₁₃	—	4	2	no	—
61	C₂×C₈×C₁₃	—	4	1	no	—
62	C₂×C₈×C₁₃	—	4	2	no	—
63	C₂×C₈×C₁₃	SD₁₆	1	2	yes	—
64	C₂×C₈×C₁₃	Q₁₆	1	2	yes	—
65	C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₁₃×C₄⋊C₄	—	2	4	no	—
67	C₁₃×C₄⋊C₄	—	2	4	no	—
68	C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₁₃×C₄⋊C₄	—	4	2	no	—
70	C₁₃×C₄⋊C₄	—	4	2	no	—
71	C₁₃×C₄⋊C₄	Q₁₆	1	2	yes	—
72	C₄²×C₁₃	—	4	1	no	—
73	C₄²×C₁₃	—	4	1	no	—
74	C₄²×C₁₃	C₂×D₄	1	2	yes	—
75	C₄²×C₁₃	#41	1	2	yes	—
76	C₂×#500	C₂×C₁₃	1	1	yes	characteristic
77	#1987	C₂×C₁₃	1	2	yes	—
78	#1939	C₂×C₁₃	1	1	yes	characteristic
79	C₂×#333	C₂×C₁₃	1	2	yes	—
80	#1277	C₂×C₁₃	1	1	yes	characteristic
81	C₂³×C₁₃	#121	1	1	yes	characteristic
82	Q₈×C₁₃	—	8	4	no	—
83	Q₈×C₁₃	—	8	4	no	—
84	C₂×C₄×C₁₃	—	2	1	no	—
85	C₂×C₄×C₁₃	—	2	1	no	—
86	C₂×C₄×C₁₃	—	2	2	no	—
87	C₂×C₄×C₁₃	—	4	1	no	—
88	C₂×C₄×C₁₃	—	4	1	no	—
89	C₂×C₄×C₁₃	—	4	4	no	—
90	C₂×C₄×C₁₃	—	4	1	no	—
91	C₂×C₄×C₁₃	—	4	1	no	—
92	C₂×C₄×C₁₃	—	4	1	no	—
93	C₂×C₄×C₁₃	—	8	2	no	—
94	C₂×C₄×C₁₃	—	8	2	no	—
95	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
96	C₂×C₄×C₁₃	#121	1	2	yes	—
97	C₂×C₄×C₁₃	#123	1	2	yes	—
98	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
99	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
101	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
102	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
103	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
104	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
105	C₂×C₄×C₁₃	#137	1	2	yes	—
106	C₈×C₁₃	—	2	2	no	—
107	C₈×C₁₃	—	2	2	no	—
108	C₈×C₁₃	—	8	1	no	—
109	C₈×C₁₃	—	8	2	no	—
110	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
111	#500	—	2	4	no	—
112	C₂×#107	—	2	1	no	—
113	C₂×#107	—	2	1	no	—
114	C₂×C₄⋊C₈	—	2	1	no	—
115	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
116	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
117	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
118	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
119	#340	—	2	2	no	—
120	#340	—	2	2	no	—
121	#336	—	2	1	no	—
122	#333	—	2	4	no	—
123	C₂²×C₁₃	#394	1	1	yes	characteristic
124	C₂²×C₁₃	#461	1	1	yes	characteristic
125	C₂²×C₁₃	#462	1	1	yes	characteristic
126	C₂²×C₁₃	#467	1	1	yes	characteristic
127	C₂²×C₁₃	#470	1	1	yes	characteristic
128	C₂²×C₁₃	#472	1	1	yes	characteristic
129	C₂²×C₁₃	#472	1	1	yes	characteristic
130	C₄×C₁₃	—	2	2	no	—
131	C₄×C₁₃	—	4	2	no	—
132	C₄×C₁₃	—	8	1	no	—
133	C₄×C₁₃	—	8	4	no	—
134	C₄×C₁₃	#448	1	1	yes	characteristic
135	C₄×C₁₃	#451	1	1	yes	characteristic
136	C₄×C₁₃	#462	1	2	yes	—
137	C₄×C₁₃	#464	1	2	yes	—
138	C₄×C₁₃	#487	1	1	yes	characteristic
139	C₄×C₁₃	#491	1	1	yes	characteristic
140	C₂²×Q₈	—	2	2	no	—
141	C₂²×C₈	—	2	1	no	—
142	C₂²×C₈	—	2	2	no	—
143	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
144	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
145	C₄⋊Q₈	—	2	2	no	—
146	C₄⋊Q₈	—	2	2	no	—
147	C₄⋊Q₈	—	2	2	no	—
148	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
149	C₂×C₄⋊C₄	—	2	2	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
152	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
153	C₂×C₄²	—	2	1	no	—
154	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
155	#107	—	2	4	no	—
156	#107	—	2	4	no	—
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	2	2	no	—
160	C₄⋊C₈	—	4	2	no	—
161	C₄×C₈	—	2	2	no	—
162	#95	—	2	1	no	—
163	C₂×C₁₃	#1675	1	1	yes	characteristic
164	C₂×C₁₃	#1676	1	1	yes	characteristic
165	C₂×C₁₃	#1695	1	1	yes	characteristic
166	C₂×C₁₃	#1696	1	1	yes	characteristic
167	C₂×C₁₃	#2043	1	1	yes	characteristic
168	C₂×C₁₃	#2045	1	1	yes	characteristic
169	C₂×C₁₃	#2056	1	1	yes	characteristic
170	C₂×Q₈	—	2	4	no	—
171	C₂×Q₈	—	4	2	no	—
172	C₂×Q₈	—	8	2	no	—
173	C₂×Q₈	—	8	2	no	—
174	C₂²×C₄	—	2	1	no	—
175	C₂²×C₄	—	2	1	no	—
176	C₂²×C₄	—	4	2	no	—
177	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
178	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
179	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
180	C₂×C₈	—	2	1	no	—
181	C₂×C₈	—	2	1	no	—
182	C₂×C₈	—	2	1	no	—
183	C₂×C₈	—	2	1	no	—
184	C₂×C₈	—	4	1	no	—
185	C₂×C₈	—	4	2	no	—
186	C₂×C₈	—	4	1	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	—	4	1	no	—
189	C₂×C₈	—	4	2	no	—
190	C₂×C₈	C₁₃×SD₁₆	1	2	yes	—
191	C₂×C₈	C₁₃×Q₁₆	1	2	yes	—
192	C₄⋊C₄	—	2	1	no	—
193	C₄⋊C₄	—	2	4	no	—
194	C₄⋊C₄	—	2	4	no	—
195	C₄⋊C₄	—	2	2	no	—
196	C₄⋊C₄	—	4	2	no	—
197	C₄⋊C₄	—	4	2	no	—
198	C₄⋊C₄	C₁₃×Q₁₆	1	2	yes	—
199	C₄²	—	4	1	no	—
200	C₄²	—	4	1	no	—
201	C₄²	C₂×D₄×C₁₃	1	2	yes	—
202	C₄²	C₁₃×#41	1	2	yes	—
203	C₁₃	#10543	1	1	yes	characteristic, direct product factor, Sylow
204	C₂³	C₁₃×#121	1	1	yes	characteristic
205	Q₈	—	8	4	no	—
206	Q₈	—	8	4	no	—
207	C₂×C₄	—	2	1	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	4	1	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	4	4	no	—
213	C₂×C₄	—	4	1	no	—
214	C₂×C₄	—	4	1	no	—
215	C₂×C₄	—	4	1	no	—
216	C₂×C₄	—	8	2	no	—
217	C₂×C₄	—	8	2	no	—
218	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
219	C₂×C₄	C₁₃×#121	1	2	yes	—
220	C₂×C₄	C₁₃×#123	1	2	yes	—
221	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
222	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
223	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
224	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
225	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
226	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
227	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
228	C₂×C₄	C₁₃×#137	1	2	yes	—
229	C₈	—	2	2	no	—
230	C₈	—	2	2	no	—
231	C₈	—	8	1	no	—
232	C₈	—	8	2	no	—
233	C₂²	C₁₃×#394	1	1	yes	characteristic
234	C₂²	C₁₃×#461	1	1	yes	characteristic
235	C₂²	C₁₃×#462	1	1	yes	characteristic
236	C₂²	C₁₃×#467	1	1	yes	characteristic
237	C₂²	C₁₃×#470	1	1	yes	characteristic
238	C₂²	C₁₃×#472	1	1	yes	characteristic
239	C₂²	C₁₃×#472	1	1	yes	characteristic
240	C₄	—	2	2	no	—
241	C₄	—	4	2	no	—
242	C₄	—	8	4	no	—
243	C₄	—	8	1	no	—
244	C₄	C₁₃×#448	1	1	yes	characteristic
245	C₄	C₁₃×#451	1	1	yes	characteristic
246	C₄	C₁₃×#462	1	2	yes	—
247	C₄	C₁₃×#464	1	2	yes	—
248	C₄	C₁₃×#487	1	1	yes	characteristic
249	C₄	C₁₃×#491	1	1	yes	characteristic
250	C₂	C₁₃×#1675	1	1	yes	characteristic
251	C₂	C₁₃×#1676	1	1	yes	characteristic
252	C₂	C₁₃×#1695	1	1	yes	characteristic
253	C₂	C₁₃×#1696	1	1	yes	characteristic
254	C₂	C₁₃×#2043	1	1	yes	characteristic
255	C₂	C₁₃×#2045	1	1	yes	characteristic
256	C₂	C₁₃×#2056	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
42. #10543	C₁₃	direct (N × H)
203. C₁₃	#10543	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×#500	2
C₁₃×#1987	2
C₁₃×#1939	2
C₂×C₁₃×#333	2
C₁₃×#1277	2
#10543	13

Subgroups — C13×#10543 #15696882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10543 #15696882