Subgroups — C₁₃×#8962 #15695301

Order 3328.

510 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2983	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1479	C₂	1	2	yes	maximal
4	C₁₃×#1461	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1276	C₂	1	2	yes	maximal
6	C₂×C₁₃×C₄⋊Q₈	C₄	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#446	—	2	4	no	—
10	C₁₃×#432	—	2	2	no	—
11	C₁₃×#431	C₂²	1	2	yes	—
12	C₁₃×#431	C₂²	1	2	yes	—
13	C₁₃×#391	C₄	1	1	yes	characteristic
14	C₁₃×#391	C₄	1	1	yes	characteristic
15	C₁₃×#389	—	2	2	no	—
16	C₁₃×#384	C₄	1	1	yes	characteristic
17	C₄×C₁₃×C₄⋊C₄	—	2	2	no	—
18	C₄³×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×Q₈⋊C₈	—	2	4	no	—
20	C₁₃×#324	—	2	2	no	—
21	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₁₃×C₄⋊Q₈	—	2	2	no	—
24	C₁₃×C₄⋊Q₈	—	2	2	no	—
25	C₄×Q₈×C₁₃	—	2	2	no	—
26	C₄×Q₈×C₁₃	—	2	2	no	—
27	C₄×Q₈×C₁₃	—	2	2	no	—
28	C₄×Q₈×C₁₃	—	2	2	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
31	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
32	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
33	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
34	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
35	C₂×C₄²×C₁₃	—	2	1	no	—
36	C₂×C₄²×C₁₃	—	2	1	no	—
37	C₂×C₄²×C₁₃	—	2	1	no	—
38	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₃	D₄	1	2	yes	—
41	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
42	C₁₃×C₄⋊C₈	—	2	4	no	—
43	C₁₃×C₄⋊C₈	—	2	2	no	—
44	C₁₃×C₄⋊C₈	D₄	1	4	yes	—
45	C₁₃×C₂²⋊C₈	—	2	2	no	—
46	C₁₃×C₂²⋊C₈	—	2	2	no	—
47	C₁₃×#97	—	2	4	no	—
48	C₄×C₈×C₁₃	—	2	2	no	—
49	C₄×C₈×C₁₃	—	2	2	no	—
50	C₁₃×#95	—	2	2	no	—
51	C₁₃×#95	—	2	2	no	—
52	#8962	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂×Q₈×C₁₃	—	2	2	no	—
54	C₂×Q₈×C₁₃	—	2	1	no	—
55	C₂×Q₈×C₁₃	—	2	1	no	—
56	C₂×Q₈×C₁₃	—	2	1	no	—
57	C₂×Q₈×C₁₃	—	2	2	no	—
58	C₂×Q₈×C₁₃	—	2	2	no	—
59	C₂×Q₈×C₁₃	—	2	2	no	—
60	C₂×Q₈×C₁₃	M₁₆	1	2	yes	—
61	C₂²×C₄×C₁₃	—	2	1	no	—
62	C₂²×C₄×C₁₃	—	2	1	no	—
63	C₂²×C₄×C₁₃	—	2	1	no	—
64	C₂²×C₄×C₁₃	—	2	1	no	—
65	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
66	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
67	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
70	C₂×C₈×C₁₃	—	2	4	no	—
71	C₂×C₈×C₁₃	—	4	2	no	—
72	C₁₃×C₄⋊C₄	—	2	8	no	—
73	C₁₃×C₄⋊C₄	—	2	2	no	—
74	C₁₃×C₄⋊C₄	—	2	4	no	—
75	C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₁₃×C₄⋊C₄	—	4	4	no	—
77	C₁₃×C₄⋊C₄	—	4	2	no	—
78	C₄²×C₁₃	—	2	4	no	—
79	C₄²×C₁₃	—	2	2	no	—
80	C₄²×C₁₃	—	2	2	no	—
81	C₄²×C₁₃	—	2	1	no	—
82	C₄²×C₁₃	—	2	2	no	—
83	C₄²×C₁₃	—	4	2	no	—
84	C₄²×C₁₃	—	4	1	no	—
85	C₄²×C₁₃	—	4	1	no	—
86	C₄²×C₁₃	M₁₆	1	2	yes	—
87	C₄²×C₁₃	C₂×D₄	1	2	yes	—
88	C₄²×C₁₃	#41	1	2	yes	—
89	#2983	C₂×C₁₃	1	1	yes	characteristic
90	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
91	#1479	C₂×C₁₃	1	2	yes	—
92	#1461	C₂×C₁₃	1	1	yes	characteristic
93	#1276	C₂×C₁₃	1	2	yes	—
94	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	Q₈×C₁₃	—	2	4	no	—
96	Q₈×C₁₃	—	4	2	no	—
97	Q₈×C₁₃	—	4	2	no	—
98	Q₈×C₁₃	—	4	2	no	—
99	C₂×C₄×C₁₃	—	2	2	no	—
100	C₂×C₄×C₁₃	—	2	2	no	—
101	C₂×C₄×C₁₃	—	2	2	no	—
102	C₂×C₄×C₁₃	—	2	2	no	—
103	C₂×C₄×C₁₃	—	2	2	no	—
104	C₂×C₄×C₁₃	—	2	2	no	—
105	C₂×C₄×C₁₃	—	2	2	no	—
106	C₂×C₄×C₁₃	—	2	2	no	—
107	C₂×C₄×C₁₃	—	2	2	no	—
108	C₂×C₄×C₁₃	—	2	2	no	—
109	C₂×C₄×C₁₃	—	4	1	no	—
110	C₂×C₄×C₁₃	—	4	1	no	—
111	C₂×C₄×C₁₃	—	4	1	no	—
112	C₂×C₄×C₁₃	—	4	1	no	—
113	C₂×C₄×C₁₃	—	4	1	no	—
114	C₂×C₄×C₁₃	—	4	2	no	—
115	C₂×C₄×C₁₃	—	4	2	no	—
116	C₂×C₄×C₁₃	—	4	1	no	—
117	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
118	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
119	C₂×C₄×C₁₃	#121	1	2	yes	—
120	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
121	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
122	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
123	C₂×C₄×C₁₃	#131	1	2	yes	—
124	C₈×C₁₃	—	4	4	no	—
125	C₈×C₁₃	—	8	2	no	—
126	C₂×C₄⋊Q₈	C₄×C₁₃	1	1	yes	characteristic
127	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
128	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
129	#446	—	2	4	no	—
130	#432	—	2	2	no	—
131	#431	C₂²×C₁₃	1	2	yes	—
132	#431	C₂²×C₁₃	1	2	yes	—
133	#391	C₄×C₁₃	1	1	yes	characteristic
134	#391	C₄×C₁₃	1	1	yes	characteristic
135	#389	—	2	2	no	—
136	#384	C₄×C₁₃	1	1	yes	characteristic
137	C₄×C₄⋊C₄	—	2	2	no	—
138	C₄³	C₂²×C₁₃	1	1	yes	characteristic
139	Q₈⋊C₈	—	2	4	no	—
140	#324	—	2	2	no	—
141	C₂²×C₁₃	—	2	1	no	—
142	C₂²×C₁₃	—	2	1	no	—
143	C₂²×C₁₃	#386	1	1	yes	characteristic
144	C₂²×C₁₃	#407	1	1	yes	characteristic
145	C₂²×C₁₃	#408	1	1	yes	characteristic
146	C₄×C₁₃	—	2	4	no	—
147	C₄×C₁₃	—	2	2	no	—
148	C₄×C₁₃	—	2	1	no	—
149	C₄×C₁₃	—	4	2	no	—
150	C₄×C₁₃	—	4	2	no	—
151	C₄×C₁₃	—	4	2	no	—
152	C₄×C₁₃	—	4	2	no	—
153	C₄×C₁₃	—	8	1	no	—
154	C₄×C₁₃	#435	1	2	yes	—
155	C₄×C₁₃	#436	1	2	yes	—
156	C₄×C₁₃	#456	1	2	yes	—
157	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
158	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
159	C₄⋊Q₈	—	2	2	no	—
160	C₄⋊Q₈	—	2	2	no	—
161	C₄×Q₈	—	2	2	no	—
162	C₄×Q₈	—	2	2	no	—
163	C₄×Q₈	—	2	2	no	—
164	C₄×Q₈	—	2	2	no	—
165	C₂×C₄⋊C₄	—	2	2	no	—
166	C₂×C₄⋊C₄	—	2	2	no	—
167	C₂×C₄⋊C₄	—	2	1	no	—
168	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
169	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
170	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
171	C₂×C₄²	—	2	1	no	—
172	C₂×C₄²	—	2	1	no	—
173	C₂×C₄²	—	2	1	no	—
174	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
175	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
176	C₂×C₄²	D₄×C₁₃	1	2	yes	—
177	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
178	C₄⋊C₈	—	2	4	no	—
179	C₄⋊C₈	—	2	2	no	—
180	C₄⋊C₈	D₄×C₁₃	1	4	yes	—
181	C₂²⋊C₈	—	2	2	no	—
182	C₂²⋊C₈	—	2	2	no	—
183	#97	—	2	4	no	—
184	C₄×C₈	—	2	2	no	—
185	C₄×C₈	—	2	2	no	—
186	#95	—	2	2	no	—
187	#95	—	2	2	no	—
188	C₂×C₁₃	—	2	1	no	—
189	C₂×C₁₃	—	2	1	no	—
190	C₂×C₁₃	#1870	1	1	yes	characteristic
191	C₂×C₁₃	#1884	1	1	yes	characteristic
192	C₂×C₁₃	#1886	1	1	yes	characteristic
193	C₂×Q₈	—	2	2	no	—
194	C₂×Q₈	—	2	1	no	—
195	C₂×Q₈	—	2	1	no	—
196	C₂×Q₈	—	2	1	no	—
197	C₂×Q₈	—	2	2	no	—
198	C₂×Q₈	—	2	2	no	—
199	C₂×Q₈	—	2	2	no	—
200	C₂×Q₈	C₁₃×M₁₆	1	2	yes	—
201	C₂²×C₄	—	2	1	no	—
202	C₂²×C₄	—	2	1	no	—
203	C₂²×C₄	—	2	1	no	—
204	C₂²×C₄	—	2	1	no	—
205	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
206	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
207	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
208	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
209	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
210	C₂×C₈	—	2	4	no	—
211	C₂×C₈	—	4	2	no	—
212	C₄⋊C₄	—	2	8	no	—
213	C₄⋊C₄	—	2	2	no	—
214	C₄⋊C₄	—	2	4	no	—
215	C₄⋊C₄	—	2	2	no	—
216	C₄⋊C₄	—	4	4	no	—
217	C₄⋊C₄	—	4	2	no	—
218	C₄²	—	2	4	no	—
219	C₄²	—	2	2	no	—
220	C₄²	—	2	2	no	—
221	C₄²	—	2	1	no	—
222	C₄²	—	2	2	no	—
223	C₄²	—	4	2	no	—
224	C₄²	—	4	1	no	—
225	C₄²	—	4	1	no	—
226	C₄²	C₁₃×M₁₆	1	2	yes	—
227	C₄²	C₂×D₄×C₁₃	1	2	yes	—
228	C₄²	C₁₃×#41	1	2	yes	—
229	C₁₃	#8962	1	1	yes	characteristic, direct product factor, Sylow
230	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
231	Q₈	—	2	4	no	—
232	Q₈	—	4	2	no	—
233	Q₈	—	4	2	no	—
234	Q₈	—	4	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	2	2	no	—
237	C₂×C₄	—	2	2	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	2	2	no	—
245	C₂×C₄	—	4	1	no	—
246	C₂×C₄	—	4	1	no	—
247	C₂×C₄	—	4	1	no	—
248	C₂×C₄	—	4	1	no	—
249	C₂×C₄	—	4	1	no	—
250	C₂×C₄	—	4	2	no	—
251	C₂×C₄	—	4	2	no	—
252	C₂×C₄	—	4	1	no	—
253	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
254	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
255	C₂×C₄	C₁₃×#121	1	2	yes	—
256	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
257	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
258	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
259	C₂×C₄	C₁₃×#131	1	2	yes	—
260	C₈	—	4	4	no	—
261	C₈	—	8	2	no	—
262	C₂²	—	2	1	no	—
263	C₂²	—	2	1	no	—
264	C₂²	C₁₃×#386	1	1	yes	characteristic
265	C₂²	C₁₃×#407	1	1	yes	characteristic
266	C₂²	C₁₃×#408	1	1	yes	characteristic
267	C₄	—	2	4	no	—
268	C₄	—	2	2	no	—
269	C₄	—	2	1	no	—
270	C₄	—	4	2	no	—
271	C₄	—	4	2	no	—
272	C₄	—	4	2	no	—
273	C₄	—	4	2	no	—
274	C₄	—	8	1	no	—
275	C₄	C₁₃×#435	1	2	yes	—
276	C₄	C₁₃×#436	1	2	yes	—
277	C₄	C₁₃×#456	1	2	yes	—
278	C₂	—	2	1	no	—
279	C₂	—	2	1	no	—
280	C₂	C₁₃×#1870	1	1	yes	characteristic
281	C₂	C₁₃×#1884	1	1	yes	characteristic
282	C₂	C₁₃×#1886	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	#120
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle	C₂²×C₁₃	#386
prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
52. #8962	C₁₃	direct (N × H)
229. C₁₃	#8962	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×#2983	2
C₄×C₁₃×C₄⋊Q₈	2
C₁₃×#1479	2
C₁₃×#1461	2
C₁₃×#1276	2
#8962	13

Subgroups — C13×#8962 #15695301

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#8962 #15695301