Subgroups — C₁₃×#21283 #15707622

Order 3328.

766 conjugacy classes of subgroups.

The subgroup lattice has 268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2320	C₂	1	2	yes	maximal
3	C₁₃×#1971	C₂	1	2	yes	maximal
4	C₁₃×#1943	C₂	1	2	yes	maximal
5	C₁₃×#1933	C₂	1	4	yes	maximal
6	C₄×C₁₃×#106	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1763	C₂	1	2	yes	maximal
8	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
11	C₄×C₁₃×Q₁₆	C₄	1	8	yes	complemented
12	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#106	C₂²	1	2	yes	—
14	C₂×C₁₃×#103	C₂²	1	4	yes	—
15	C₂×C₁₃×#103	C₂²	1	2	yes	—
16	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#97	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#391	C₂²	1	4	yes	—
21	C₁₃×#389	C₂²	1	4	yes	—
22	C₁₃×#387	—	2	4	no	—
23	C₁₃×#383	—	2	2	no	—
24	C₁₃×#382	—	2	2	no	—
25	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₁₃×#376	C₂²	1	1	yes	characteristic
27	C₁₃×#340	C₂²	1	4	yes	—
28	C₁₃×#340	C₂²	1	2	yes	—
29	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
30	C₂×C₁₃×Q₁₆	—	2	4	no	—
31	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	—
32	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
33	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
34	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
35	C₄×Q₈×C₁₃	—	2	4	no	—
36	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	—
37	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
38	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
39	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
40	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
41	C₂×C₄²×C₁₃	—	2	2	no	—
42	C₂×C₄²×C₁₃	—	2	2	no	—
43	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
44	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
45	C₁₃×#107	C₂×C₄	1	4	yes	—
46	C₁₃×#106	—	2	4	no	—
47	C₁₃×#103	—	2	8	no	—
48	C₁₃×#103	C₂×C₄	1	8	yes	—
49	C₁₃×#97	—	2	4	no	—
50	C₁₃×#97	—	2	2	no	—
51	C₄×C₈×C₁₃	—	2	4	no	—
52	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
53	C₁₃×#95	—	2	2	no	—
54	C₁₃×#95	—	2	4	no	—
55	C₁₃×#95	—	2	4	no	—
56	C₁₃×#95	—	2	4	no	—
57	C₁₃×#95	D₄	1	2	yes	—
58	C₁₃×#95	D₄	1	2	yes	—
59	#21283	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂×Q₈×C₁₃	—	2	2	no	—
61	C₂×Q₈×C₁₃	—	2	4	no	—
62	C₂×Q₈×C₁₃	—	2	4	no	—
63	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
64	C₂²×C₄×C₁₃	—	2	2	no	—
65	C₂²×C₄×C₁₃	—	2	2	no	—
66	C₂²×C₄×C₁₃	—	2	4	no	—
67	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
68	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
71	C₁₃×Q₁₆	—	2	8	no	—
72	C₂×C₈×C₁₃	—	2	2	no	—
73	C₂×C₈×C₁₃	—	2	2	no	—
74	C₂×C₈×C₁₃	—	2	2	no	—
75	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
76	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
77	C₂×C₈×C₁₃	#41	1	4	yes	—
78	C₂×C₈×C₁₃	#41	1	4	yes	—
79	C₁₃×C₄⋊C₄	—	2	8	no	—
80	C₁₃×C₄⋊C₄	—	2	2	no	—
81	C₁₃×C₄⋊C₄	—	2	4	no	—
82	C₁₃×C₄⋊C₄	—	2	4	no	—
83	C₁₃×C₄⋊C₄	—	8	4	no	—
84	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
85	C₄²×C₁₃	—	2	8	no	—
86	C₄²×C₁₃	—	2	2	no	—
87	C₄²×C₁₃	—	2	2	no	—
88	C₄²×C₁₃	—	8	2	no	—
89	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
90	C₄²×C₁₃	#41	1	2	yes	—
91	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic
92	#2320	C₂×C₁₃	1	2	yes	—
93	#1971	C₂×C₁₃	1	2	yes	—
94	#1943	C₂×C₁₃	1	2	yes	—
95	#1933	C₂×C₁₃	1	4	yes	—
96	C₄×#106	C₂×C₁₃	1	1	yes	characteristic
97	#1763	C₂×C₁₃	1	2	yes	—
98	#1726	C₂×C₁₃	1	1	yes	characteristic
99	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
100	Q₈×C₁₃	—	2	4	no	—
101	Q₈×C₁₃	—	2	4	no	—
102	Q₈×C₁₃	—	4	4	no	—
103	C₂×C₄×C₁₃	—	2	2	no	—
104	C₂×C₄×C₁₃	—	2	2	no	—
105	C₂×C₄×C₁₃	—	2	4	no	—
106	C₂×C₄×C₁₃	—	2	4	no	—
107	C₂×C₄×C₁₃	—	2	4	no	—
108	C₂×C₄×C₁₃	—	2	4	no	—
109	C₂×C₄×C₁₃	—	2	4	no	—
110	C₂×C₄×C₁₃	—	4	4	no	—
111	C₂×C₄×C₁₃	—	4	2	no	—
112	C₂×C₄×C₁₃	—	4	2	no	—
113	C₂×C₄×C₁₃	—	4	4	no	—
114	C₂×C₄×C₁₃	—	4	4	no	—
115	C₂×C₄×C₁₃	—	4	4	no	—
116	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
117	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
118	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
119	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
120	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
121	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
122	C₈×C₁₃	—	2	2	no	—
123	C₈×C₁₃	—	2	4	no	—
124	C₈×C₁₃	#117	1	4	yes	—
125	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
126	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
127	C₄×Q₁₆	C₄×C₁₃	1	8	yes	complemented
128	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
129	C₂×#106	C₂²×C₁₃	1	2	yes	—
130	C₂×#103	C₂²×C₁₃	1	4	yes	—
131	C₂×#103	C₂²×C₁₃	1	2	yes	—
132	C₂×#97	C₂²×C₁₃	1	2	yes	—
133	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
134	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
135	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
136	#391	C₂²×C₁₃	1	4	yes	—
137	#389	C₂²×C₁₃	1	4	yes	—
138	#387	—	2	4	no	—
139	#383	—	2	2	no	—
140	#382	—	2	2	no	—
141	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
142	#376	C₂²×C₁₃	1	1	yes	characteristic
143	#340	C₂²×C₁₃	1	2	yes	—
144	#340	C₂²×C₁₃	1	4	yes	—
145	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
146	C₂²×C₁₃	#532	1	2	yes	—
147	C₂²×C₁₃	#577	1	2	yes	—
148	C₂²×C₁₃	#578	1	2	yes	—
149	C₄×C₁₃	—	2	2	no	—
150	C₄×C₁₃	—	2	2	no	—
151	C₄×C₁₃	—	4	4	no	—
152	C₄×C₁₃	—	4	4	no	—
153	C₄×C₁₃	—	4	4	no	—
154	C₄×C₁₃	—	8	4	no	—
155	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
156	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
157	C₄×C₁₃	#529	1	2	yes	—
158	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
159	C₂×Q₁₆	—	2	4	no	—
160	C₂×Q₁₆	C₂×C₄×C₁₃	1	4	yes	—
161	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
162	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
163	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
164	C₄×Q₈	—	2	4	no	—
165	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	—
166	C₂×C₄⋊C₄	—	2	2	no	—
167	C₂×C₄⋊C₄	—	2	4	no	—
168	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
169	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
170	C₂×C₄²	—	2	2	no	—
171	C₂×C₄²	—	2	2	no	—
172	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
173	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
174	#107	C₂×C₄×C₁₃	1	4	yes	—
175	#106	—	2	4	no	—
176	#103	—	2	8	no	—
177	#103	C₂×C₄×C₁₃	1	8	yes	—
178	#97	—	2	4	no	—
179	#97	—	2	2	no	—
180	C₄×C₈	—	2	4	no	—
181	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
182	#95	—	2	2	no	—
183	#95	—	2	4	no	—
184	#95	—	2	4	no	—
185	#95	—	2	4	no	—
186	#95	D₄×C₁₃	1	2	yes	—
187	#95	D₄×C₁₃	1	2	yes	—
188	C₂×C₁₃	#2293	1	1	yes	characteristic
189	C₂×C₁₃	#2950	1	1	yes	characteristic
190	C₂×C₁₃	#2952	1	1	yes	characteristic
191	C₂×C₁₃	#3178	1	4	yes	—
192	C₂×Q₈	—	2	2	no	—
193	C₂×Q₈	—	2	4	no	—
194	C₂×Q₈	—	2	4	no	—
195	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
196	C₂²×C₄	—	2	2	no	—
197	C₂²×C₄	—	2	2	no	—
198	C₂²×C₄	—	2	4	no	—
199	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
200	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
201	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
202	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
203	Q₁₆	—	2	8	no	—
204	C₂×C₈	—	2	2	no	—
205	C₂×C₈	—	2	2	no	—
206	C₂×C₈	—	2	2	no	—
207	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
208	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
209	C₂×C₈	C₁₃×#41	1	4	yes	—
210	C₂×C₈	C₁₃×#41	1	4	yes	—
211	C₄⋊C₄	—	2	8	no	—
212	C₄⋊C₄	—	2	2	no	—
213	C₄⋊C₄	—	2	4	no	—
214	C₄⋊C₄	—	2	4	no	—
215	C₄⋊C₄	—	8	4	no	—
216	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
217	C₄²	—	2	8	no	—
218	C₄²	—	2	2	no	—
219	C₄²	—	2	2	no	—
220	C₄²	—	8	2	no	—
221	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
222	C₄²	C₁₃×#41	1	2	yes	—
223	C₁₃	#21283	1	1	yes	characteristic, direct product factor, Sylow
224	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
225	Q₈	—	2	4	no	—
226	Q₈	—	2	4	no	—
227	Q₈	—	4	4	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	4	no	—
231	C₂×C₄	—	2	4	no	—
232	C₂×C₄	—	2	4	no	—
233	C₂×C₄	—	2	4	no	—
234	C₂×C₄	—	2	4	no	—
235	C₂×C₄	—	4	4	no	—
236	C₂×C₄	—	4	2	no	—
237	C₂×C₄	—	4	2	no	—
238	C₂×C₄	—	4	4	no	—
239	C₂×C₄	—	4	4	no	—
240	C₂×C₄	—	4	4	no	—
241	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
242	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
243	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
244	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
245	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
246	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
247	C₈	—	2	2	no	—
248	C₈	—	2	4	no	—
249	C₈	C₁₃×#117	1	4	yes	—
250	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
251	C₂²	C₁₃×#532	1	2	yes	—
252	C₂²	C₁₃×#577	1	2	yes	—
253	C₂²	C₁₃×#578	1	2	yes	—
254	C₄	—	2	2	no	—
255	C₄	—	2	2	no	—
256	C₄	—	4	4	no	—
257	C₄	—	4	4	no	—
258	C₄	—	4	4	no	—
259	C₄	—	8	4	no	—
260	C₄	C₂×C₁₃×#117	1	1	yes	characteristic
261	C₄	C₄×C₁₃×#41	1	1	yes	characteristic
262	C₄	C₁₃×#529	1	2	yes	—
263	C₂	C₁₃×#2293	1	1	yes	characteristic
264	C₂	C₁₃×#2950	1	1	yes	characteristic
265	C₂	C₁₃×#2952	1	1	yes	characteristic
266	C₂	C₁₃×#3178	1	4	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₁₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
11. C₄×C₁₃×Q₁₆	C₄	semidirect
59. #21283	C₁₃	direct (N × H)
127. C₄×Q₁₆	C₄×C₁₃	semidirect
223. C₁₃	#21283	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×C₁₃×Q₁₆	2
C₁₃×#2320	2
C₁₃×#1971	2
C₁₃×#1943	2
C₁₃×#1933	2
C₄×C₁₃×#106	2
C₁₃×#1763	2
C₁₃×#1726	2
#21283	13

Subgroups — C13×#21283 #15707622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21283 #15707622