Subgroups — C₁₃×#11659 #15697998

Order 3328.

364 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2162	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#1568	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1332	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1331	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#135	C₄	1	1	yes	characteristic
7	C₄×C₁₃×#41	—	2	1	no	—
8	C₄×C₁₃×Q₁₆	C₄	1	1	yes	characteristic
9	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
10	C₄×C₁₃×SD₁₆	—	2	1	no	—
11	C₄×C₁₃×SD₁₆	—	2	1	no	—
12	C₄×C₁₃×D₈	C₄	1	1	yes	characteristic
13	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
14	C₁₃×#432	—	2	1	no	—
15	C₁₃×#427	C₄	1	1	yes	characteristic
16	C₁₃×#416	—	2	1	no	—
17	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×C₄⋊C₁₆	—	2	1	no	—
19	C₁₃×C₂²⋊C₁₆	—	2	1	no	—
20	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
21	C₁₃×#335	C₂²	1	2	yes	—
22	C₁₃×#334	—	2	1	no	—
23	C₂×C₁₃×#41	—	2	1	no	—
24	C₁₃×#135	—	2	2	no	—
25	C₁₃×#135	—	2	2	no	—
26	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
27	C₂×C₁₃×SD₁₆	—	2	1	no	—
28	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
31	C₄×Q₈×C₁₃	—	2	1	no	—
32	C₄×Q₈×C₁₃	—	2	1	no	—
33	C₄×D₄×C₁₃	—	2	1	no	—
34	C₄×D₄×C₁₃	—	2	1	no	—
35	C₄×D₄×C₁₃	—	4	1	no	—
36	C₄×D₄×C₁₃	—	4	1	no	—
37	C₁₃×#117	—	2	1	no	—
38	C₁₃×#117	—	4	1	no	—
39	C₂×C₄²×C₁₃	—	4	1	no	—
40	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
41	C₂×C₁₃×C₁₆	—	2	2	no	—
42	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
43	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
44	C₁₃×#106	—	2	1	no	—
45	C₁₃×C₄⋊C₈	—	2	2	no	—
46	C₁₃×#103	—	2	1	no	—
47	C₁₃×#103	—	2	1	no	—
48	C₁₃×#102	—	2	1	no	—
49	C₁₃×#102	—	2	1	no	—
50	C₁₃×C₂²⋊C₈	—	4	1	no	—
51	C₁₃×#97	—	4	1	no	—
52	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
54	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
55	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	#11659	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₁₃×#41	—	2	4	no	—
58	C₁₃×#41	—	4	2	no	—
59	C₂×Q₈×C₁₃	—	2	1	no	—
60	C₂×D₄×C₁₃	—	2	1	no	—
61	C₂×D₄×C₁₃	—	4	1	no	—
62	C₂²×C₄×C₁₃	—	4	1	no	—
63	C₂²×C₄×C₁₃	—	4	1	no	—
64	C₂²×C₄×C₁₃	—	4	1	no	—
65	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	SD₁₆	1	1	yes	characteristic
68	C₁₃×Q₁₆	—	2	1	no	—
69	C₁₃×Q₁₆	M₁₆	1	2	yes	—
70	C₁₃×SD₁₆	—	2	4	no	—
71	C₁₃×D₈	—	2	1	no	—
72	C₁₃×D₈	M₁₆	1	2	yes	—
73	C₂×C₈×C₁₃	—	2	1	no	—
74	C₂×C₈×C₁₃	—	2	1	no	—
75	C₂×C₈×C₁₃	—	4	1	no	—
76	C₂×C₈×C₁₃	—	4	2	no	—
77	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
80	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
81	C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₁₃×C₄⋊C₄	—	4	1	no	—
84	C₁₃×C₄⋊C₄	—	4	1	no	—
85	C₁₃×C₂²⋊C₄	—	4	1	no	—
86	C₁₃×C₂²⋊C₄	—	4	1	no	—
87	C₁₃×C₂²⋊C₄	—	4	1	no	—
88	C₄²×C₁₃	—	4	1	no	—
89	C₄²×C₁₃	—	4	1	no	—
90	C₄²×C₁₃	—	4	1	no	—
91	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₄²×C₁₃	D₈	1	1	yes	characteristic
93	C₄²×C₁₃	SD₁₆	1	1	yes	characteristic
94	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₁₃×C₁₆	—	4	2	no	—
96	C₄×#135	C₂×C₁₃	1	1	yes	characteristic
97	#2162	C₂×C₁₃	1	1	yes	characteristic, complemented
98	#1568	C₂×C₁₃	1	1	yes	characteristic, complemented
99	#1332	C₂×C₁₃	1	2	yes	complemented
100	#1331	C₂×C₁₃	1	2	yes	complemented
101	C₂³×C₁₃	—	4	1	no	—
102	C₂³×C₁₃	#102	1	1	yes	characteristic
103	Q₈×C₁₃	—	2	2	no	—
104	Q₈×C₁₃	—	4	1	no	—
105	D₄×C₁₃	—	2	2	no	—
106	D₄×C₁₃	—	4	4	no	—
107	D₄×C₁₃	—	4	1	no	—
108	C₂×C₄×C₁₃	—	2	1	no	—
109	C₂×C₄×C₁₃	—	2	1	no	—
110	C₂×C₄×C₁₃	—	2	2	no	—
111	C₂×C₄×C₁₃	—	4	1	no	—
112	C₂×C₄×C₁₃	—	4	4	no	—
113	C₂×C₄×C₁₃	—	4	1	no	—
114	C₂×C₄×C₁₃	—	4	1	no	—
115	C₂×C₄×C₁₃	—	4	1	no	—
116	C₂×C₄×C₁₃	—	8	2	no	—
117	C₂×C₄×C₁₃	—	8	2	no	—
118	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
119	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
120	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
121	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
123	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
124	C₈×C₁₃	—	2	1	no	—
125	C₈×C₁₃	—	2	1	no	—
126	C₈×C₁₃	—	2	1	no	—
127	C₈×C₁₃	—	8	2	no	—
128	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
129	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
130	C₂×#135	C₄×C₁₃	1	1	yes	characteristic
131	C₄×#41	—	2	1	no	—
132	C₄×Q₁₆	C₄×C₁₃	1	1	yes	characteristic
133	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
134	C₄×SD₁₆	—	2	1	no	—
135	C₄×SD₁₆	—	2	1	no	—
136	C₄×D₈	C₄×C₁₃	1	1	yes	characteristic
137	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
138	#432	—	2	1	no	—
139	#427	C₄×C₁₃	1	1	yes	characteristic
140	#416	—	2	1	no	—
141	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
142	C₄⋊C₁₆	—	2	1	no	—
143	C₂²⋊C₁₆	—	2	1	no	—
144	C₄×C₁₆	C₂²×C₁₃	1	2	yes	—
145	#335	C₂²×C₁₃	1	2	yes	—
146	#334	—	2	1	no	—
147	C₂²×C₁₃	—	2	1	no	—
148	C₂²×C₁₃	—	2	1	no	—
149	C₂²×C₁₃	—	2	1	no	—
150	C₂²×C₁₃	—	4	2	no	—
151	C₂²×C₁₃	—	8	1	no	—
152	C₂²×C₁₃	—	8	1	no	—
153	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
154	C₄×C₁₃	—	2	1	no	—
155	C₄×C₁₃	—	2	1	no	—
156	C₄×C₁₃	—	2	1	no	—
157	C₄×C₁₃	—	2	1	no	—
158	C₄×C₁₃	—	4	2	no	—
159	C₄×C₁₃	—	8	1	no	—
160	C₄×C₁₃	—	8	1	no	—
161	C₄×C₁₃	#407	1	1	yes	characteristic
162	C₄×C₁₃	#421	1	1	yes	characteristic
163	C₄×C₁₃	#508	1	2	yes	—
164	C₂×#41	—	2	1	no	—
165	#135	—	2	2	no	—
166	#135	—	2	2	no	—
167	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
168	C₂×SD₁₆	—	2	1	no	—
169	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
170	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
171	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
172	C₄×Q₈	—	2	1	no	—
173	C₄×Q₈	—	2	1	no	—
174	C₄×D₄	—	2	1	no	—
175	C₄×D₄	—	2	1	no	—
176	C₄×D₄	—	4	1	no	—
177	C₄×D₄	—	4	1	no	—
178	#117	—	2	1	no	—
179	#117	—	4	1	no	—
180	C₂×C₄²	—	4	1	no	—
181	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
182	C₂×C₁₆	—	2	2	no	—
183	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
184	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
185	#106	—	2	1	no	—
186	C₄⋊C₈	—	2	2	no	—
187	#103	—	2	1	no	—
188	#103	—	2	1	no	—
189	#102	—	2	1	no	—
190	#102	—	2	1	no	—
191	C₂²⋊C₈	—	4	1	no	—
192	#97	—	4	1	no	—
193	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
194	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
195	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
196	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
197	C₂×C₁₃	—	4	1	no	—
198	C₂×C₁₃	—	8	2	no	—
199	C₂×C₁₃	#1486	1	1	yes	characteristic
200	C₂×C₁₃	#2138	1	1	yes	characteristic
201	C₂×C₁₃	#2143	1	1	yes	characteristic
202	#41	—	2	4	no	—
203	#41	—	4	2	no	—
204	C₂×Q₈	—	2	1	no	—
205	C₂×D₄	—	2	1	no	—
206	C₂×D₄	—	4	1	no	—
207	C₂²×C₄	—	4	1	no	—
208	C₂²×C₄	—	4	1	no	—
209	C₂²×C₄	—	4	1	no	—
210	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
212	C₂²×C₄	C₁₃×SD₁₆	1	1	yes	characteristic
213	Q₁₆	—	2	1	no	—
214	Q₁₆	C₁₃×M₁₆	1	2	yes	—
215	SD₁₆	—	2	4	no	—
216	D₈	—	2	1	no	—
217	D₈	C₁₃×M₁₆	1	2	yes	—
218	C₂×C₈	—	2	1	no	—
219	C₂×C₈	—	2	1	no	—
220	C₂×C₈	—	4	1	no	—
221	C₂×C₈	—	4	2	no	—
222	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
225	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
226	C₄⋊C₄	—	2	1	no	—
227	C₄⋊C₄	—	2	1	no	—
228	C₄⋊C₄	—	4	1	no	—
229	C₄⋊C₄	—	4	1	no	—
230	C₂²⋊C₄	—	4	1	no	—
231	C₂²⋊C₄	—	4	1	no	—
232	C₂²⋊C₄	—	4	1	no	—
233	C₄²	—	4	1	no	—
234	C₄²	—	4	1	no	—
235	C₄²	—	4	1	no	—
236	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
237	C₄²	C₁₃×D₈	1	1	yes	characteristic
238	C₄²	C₁₃×SD₁₆	1	1	yes	characteristic
239	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
240	C₁₆	—	4	2	no	—
241	C₁₃	#11659	1	1	yes	characteristic, direct product factor, Sylow
242	C₂³	—	4	1	no	—
243	C₂³	C₁₃×#102	1	1	yes	characteristic
244	Q₈	—	2	2	no	—
245	Q₈	—	4	1	no	—
246	D₄	—	2	2	no	—
247	D₄	—	4	4	no	—
248	D₄	—	4	1	no	—
249	C₂×C₄	—	2	1	no	—
250	C₂×C₄	—	2	1	no	—
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	4	1	no	—
253	C₂×C₄	—	4	4	no	—
254	C₂×C₄	—	4	1	no	—
255	C₂×C₄	—	4	1	no	—
256	C₂×C₄	—	4	1	no	—
257	C₂×C₄	—	8	2	no	—
258	C₂×C₄	—	8	2	no	—
259	C₂×C₄	C₁₃×#102	1	1	yes	characteristic
260	C₂×C₄	C₁₃×#102	1	1	yes	characteristic
261	C₂×C₄	C₁₃×#102	1	1	yes	characteristic
262	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
264	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
265	C₈	—	2	1	no	—
266	C₈	—	2	1	no	—
267	C₈	—	2	1	no	—
268	C₈	—	8	2	no	—
269	C₈	C₂×C₁₃×M₁₆	1	1	yes	characteristic
270	C₈	C₂×C₁₃×M₁₆	1	1	yes	characteristic
271	C₂²	—	2	1	no	—
272	C₂²	—	2	1	no	—
273	C₂²	—	2	1	no	—
274	C₂²	—	4	2	no	—
275	C₂²	—	8	1	no	—
276	C₂²	—	8	1	no	—
277	C₂²	C₂×C₁₃×#102	1	1	yes	characteristic
278	C₄	—	2	1	no	—
279	C₄	—	2	1	no	—
280	C₄	—	2	1	no	—
281	C₄	—	2	1	no	—
282	C₄	—	4	2	no	—
283	C₄	—	8	1	no	—
284	C₄	—	8	1	no	—
285	C₄	C₁₃×#407	1	1	yes	characteristic
286	C₄	C₁₃×#421	1	1	yes	characteristic
287	C₄	C₁₃×#508	1	2	yes	—
288	C₂	—	4	1	no	—
289	C₂	—	8	2	no	—
290	C₂	C₁₃×#1486	1	1	yes	characteristic
291	C₂	C₁₃×#2138	1	1	yes	characteristic
292	C₂	C₁₃×#2143	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₄×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×#102
prime radical	C₂×C₁₃×#135	C₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2162	C₂	semidirect
3. C₁₃×#1568	C₂	semidirect
4. C₁₃×#1332	C₂	semidirect
5. C₁₃×#1331	C₂	semidirect
56. #11659	C₁₃	direct (N × H)
97. #2162	C₂×C₁₃	semidirect
98. #1568	C₂×C₁₃	semidirect
99. #1332	C₂×C₁₃	semidirect
100. #1331	C₂×C₁₃	semidirect
241. C₁₃	#11659	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₁₃×#135	2
C₁₃×#2162	2
C₁₃×#1568	2
C₁₃×#1332	2
C₁₃×#1331	2
#11659	13

Subgroups — C13×#11659 #15697998

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#11659 #15697998