Subgroups — C₁₃×#13064 #15699403

Order 3328.

488 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3050	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#359	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1810	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1382	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×#525	—	2	1	no	—
9	C₂×C₁₃×M₃₂	—	2	2	no	—
10	C₂×C₁₃×M₃₂	—	2	4	no	—
11	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
12	C₁₃×#467	C₄	1	2	yes	—
13	C₁₃×#466	C₄	1	2	yes	—
14	C₁₃×#465	—	2	2	no	—
15	C₂×C₁₃×#108	C₂²	1	2	yes	—
16	C₁₃×#427	C₂²	1	1	yes	characteristic
17	C₁₃×#416	—	2	1	no	—
18	C₁₃×#407	—	2	1	no	—
19	C₁₃×#359	—	2	4	no	—
20	C₁₃×#341	—	2	1	no	—
21	C₂×C₁₃×#41	—	2	1	no	—
22	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
23	C₁₃×#135	—	2	2	no	—
24	C₁₃×#135	—	2	2	no	—
25	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
26	C₂×C₁₃×SD₁₆	—	2	1	no	—
27	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
28	C₂×C₁₃×M₁₆	—	2	2	no	—
29	C₂²×C₈×C₁₃	—	2	2	no	—
30	C₂²×C₈×C₁₃	—	2	2	no	—
31	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₃	D₄	1	2	yes	—
34	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
35	C₁₃×#123	—	4	1	no	—
36	C₁₃×C₂²⋊Q₈	—	2	2	no	—
37	C₁₃×#121	—	2	2	no	—
38	C₁₃×#120	—	4	1	no	—
39	C₄×D₄×C₁₃	—	4	2	no	—
40	C₁₃×#117	—	2	1	no	—
41	C₁₃×M₃₂	—	2	8	no	—
42	C₂×C₁₃×C₁₆	—	2	2	no	—
43	C₂×C₁₃×C₁₆	—	2	2	no	—
44	C₂×C₁₃×C₁₆	D₄	1	4	yes	complemented
45	C₁₃×#108	—	2	2	no	—
46	C₁₃×#108	—	2	2	no	—
47	C₁₃×#107	C₂×C₄	1	2	yes	—
48	C₁₃×#106	—	2	1	no	—
49	C₁₃×#103	—	2	2	no	—
50	C₁₃×#102	—	2	2	no	—
51	C₁₃×C₂²⋊C₈	—	4	2	no	—
52	#13064	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂⁴×C₁₃	SD₁₆	1	1	yes	characteristic
54	C₁₃×#41	—	4	2	no	—
55	C₁₃×#41	—	4	2	no	—
56	C₂×Q₈×C₁₃	—	2	1	no	—
57	C₂×D₄×C₁₃	—	2	1	no	—
58	C₂×D₄×C₁₃	—	4	2	no	—
59	C₂×D₄×C₁₃	—	4	1	no	—
60	C₂²×C₄×C₁₃	—	2	2	no	—
61	C₂²×C₄×C₁₃	—	2	2	no	—
62	C₂²×C₄×C₁₃	—	4	1	no	—
63	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₁₃	D₈	1	2	yes	—
65	C₂²×C₄×C₁₃	SD₁₆	1	1	yes	characteristic
66	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
67	C₁₃×Q₁₆	—	2	2	no	—
68	C₁₃×SD₁₆	—	4	1	no	—
69	C₁₃×SD₁₆	—	4	1	no	—
70	C₁₃×D₈	—	2	2	no	—
71	C₁₃×M₁₆	—	4	2	no	—
72	C₁₃×M₁₆	—	4	2	no	—
73	C₂×C₈×C₁₃	—	2	2	no	—
74	C₂×C₈×C₁₃	—	2	4	no	—
75	C₂×C₈×C₁₃	—	2	2	no	—
76	C₂×C₈×C₁₃	—	2	2	no	—
77	C₂×C₈×C₁₃	—	4	2	no	—
78	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
79	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
80	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
81	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
82	C₂×C₈×C₁₃	#41	1	2	yes	—
83	C₁₃×C₄⋊C₄	—	2	2	no	—
84	C₁₃×C₄⋊C₄	—	4	2	no	—
85	C₁₃×C₂²⋊C₄	—	4	2	no	—
86	C₁₃×C₂²⋊C₄	—	4	1	no	—
87	C₁₃×C₂²⋊C₄	—	4	2	no	—
88	C₄²×C₁₃	—	4	1	no	—
89	C₁₃×C₁₆	—	2	4	no	—
90	C₂²×M₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
91	#3050	C₂×C₁₃	1	1	yes	characteristic
92	C₂×#359	C₂×C₁₃	1	2	yes	complemented
93	#1810	C₂×C₁₃	1	1	yes	characteristic, complemented
94	#1382	C₂×C₁₃	1	2	yes	complemented
95	C₂³×C₁₃	—	2	2	no	—
96	C₂³×C₁₃	—	4	2	no	—
97	C₂³×C₁₃	—	4	1	no	—
98	C₂³×C₁₃	#102	1	2	yes	—
99	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
100	Q₈×C₁₃	—	4	1	no	—
101	Q₈×C₁₃	—	4	1	no	—
102	D₄×C₁₃	—	4	1	no	—
103	D₄×C₁₃	—	4	1	no	—
104	D₄×C₁₃	—	8	4	no	—
105	D₄×C₁₃	—	8	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	—	2	4	no	—
110	C₂×C₄×C₁₃	—	4	2	no	—
111	C₂×C₄×C₁₃	—	4	1	no	—
112	C₂×C₄×C₁₃	—	8	2	no	—
113	C₂×C₄×C₁₃	#102	1	2	yes	—
114	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₂×C₄×C₁₃	#121	1	2	yes	—
116	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
117	C₂×C₄×C₁₃	#135	1	2	yes	—
118	C₈×C₁₃	—	2	2	no	—
119	C₈×C₁₃	—	8	2	no	—
120	C₈×C₁₃	C₄×D₄	1	2	yes	—
121	C₈×C₁₃	#120	1	1	yes	characteristic
122	C₈×C₁₃	#123	1	1	yes	characteristic
123	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
124	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
125	#525	—	2	1	no	—
126	C₂×M₃₂	—	2	2	no	—
127	C₂×M₃₂	—	2	4	no	—
128	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
129	#467	C₄×C₁₃	1	2	yes	—
130	#466	C₄×C₁₃	1	2	yes	—
131	#465	—	2	2	no	—
132	C₂×#108	C₂²×C₁₃	1	2	yes	—
133	#427	C₂²×C₁₃	1	1	yes	characteristic
134	#416	—	2	1	no	—
135	#407	—	2	1	no	—
136	#359	—	2	4	no	—
137	#341	—	2	1	no	—
138	C₂²×C₁₃	—	2	2	no	—
139	C₂²×C₁₃	—	2	2	no	—
140	C₂²×C₁₃	—	2	2	no	—
141	C₂²×C₁₃	—	2	2	no	—
142	C₂²×C₁₃	—	4	4	no	—
143	C₂²×C₁₃	—	8	2	no	—
144	C₂²×C₁₃	—	8	1	no	—
145	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
146	C₂²×C₁₃	#465	1	2	yes	—
147	C₄×C₁₃	—	2	2	no	—
148	C₄×C₁₃	—	8	2	no	—
149	C₄×C₁₃	—	8	1	no	—
150	C₄×C₁₃	#386	1	1	yes	characteristic
151	C₄×C₁₃	#416	1	1	yes	characteristic
152	C₄×C₁₃	#466	1	2	yes	—
153	C₂×#41	—	2	1	no	—
154	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
155	#135	—	2	2	no	—
156	#135	—	2	2	no	—
157	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
158	C₂×SD₁₆	—	2	1	no	—
159	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
160	C₂×M₁₆	—	2	2	no	—
161	C₂²×C₈	—	2	2	no	—
162	C₂²×C₈	—	2	2	no	—
163	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
164	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
165	C₂²×C₈	D₄×C₁₃	1	2	yes	—
166	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
167	#123	—	4	1	no	—
168	C₂²⋊Q₈	—	2	2	no	—
169	#121	—	2	2	no	—
170	#120	—	4	1	no	—
171	C₄×D₄	—	4	2	no	—
172	#117	—	2	1	no	—
173	M₃₂	—	2	8	no	—
174	C₂×C₁₆	—	2	2	no	—
175	C₂×C₁₆	—	2	2	no	—
176	C₂×C₁₆	D₄×C₁₃	1	4	yes	complemented
177	#108	—	2	2	no	—
178	#108	—	2	2	no	—
179	#107	C₂×C₄×C₁₃	1	2	yes	—
180	#106	—	2	1	no	—
181	#103	—	2	2	no	—
182	#102	—	2	2	no	—
183	C₂²⋊C₈	—	4	2	no	—
184	C₂×C₁₃	—	2	2	no	—
185	C₂×C₁₃	—	4	2	no	—
186	C₂×C₁₃	—	16	1	no	—
187	C₂×C₁₃	#1893	1	1	yes	characteristic
188	C₂×C₁₃	#2143	1	2	yes	—
189	C₂⁴	C₁₃×SD₁₆	1	1	yes	characteristic
190	#41	—	4	2	no	—
191	#41	—	4	2	no	—
192	C₂×Q₈	—	2	1	no	—
193	C₂×D₄	—	2	1	no	—
194	C₂×D₄	—	4	2	no	—
195	C₂×D₄	—	4	1	no	—
196	C₂²×C₄	—	2	2	no	—
197	C₂²×C₄	—	2	2	no	—
198	C₂²×C₄	—	4	1	no	—
199	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
200	C₂²×C₄	C₁₃×D₈	1	2	yes	—
201	C₂²×C₄	C₁₃×SD₁₆	1	1	yes	characteristic
202	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
203	Q₁₆	—	2	2	no	—
204	SD₁₆	—	4	1	no	—
205	SD₁₆	—	4	1	no	—
206	D₈	—	2	2	no	—
207	M₁₆	—	4	2	no	—
208	M₁₆	—	4	2	no	—
209	C₂×C₈	—	2	2	no	—
210	C₂×C₈	—	2	4	no	—
211	C₂×C₈	—	2	2	no	—
212	C₂×C₈	—	2	2	no	—
213	C₂×C₈	—	4	2	no	—
214	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
215	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
216	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
217	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
218	C₂×C₈	C₁₃×#41	1	2	yes	—
219	C₄⋊C₄	—	2	2	no	—
220	C₄⋊C₄	—	4	2	no	—
221	C₂²⋊C₄	—	4	2	no	—
222	C₂²⋊C₄	—	4	1	no	—
223	C₂²⋊C₄	—	4	2	no	—
224	C₄²	—	4	1	no	—
225	C₁₆	—	2	4	no	—
226	C₁₃	#13064	1	1	yes	characteristic, direct product factor, Sylow
227	C₂³	—	2	2	no	—
228	C₂³	—	4	2	no	—
229	C₂³	—	4	1	no	—
230	C₂³	C₁₃×#102	1	2	yes	—
231	C₂³	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
232	Q₈	—	4	1	no	—
233	Q₈	—	4	1	no	—
234	D₄	—	4	1	no	—
235	D₄	—	4	1	no	—
236	D₄	—	8	4	no	—
237	D₄	—	8	2	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	4	no	—
242	C₂×C₄	—	4	2	no	—
243	C₂×C₄	—	4	1	no	—
244	C₂×C₄	—	8	2	no	—
245	C₂×C₄	C₁₃×#102	1	2	yes	—
246	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₄	C₁₃×#121	1	2	yes	—
248	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
249	C₂×C₄	C₁₃×#135	1	2	yes	—
250	C₈	—	2	2	no	—
251	C₈	—	8	2	no	—
252	C₈	C₄×D₄×C₁₃	1	2	yes	—
253	C₈	C₁₃×#120	1	1	yes	characteristic
254	C₈	C₁₃×#123	1	1	yes	characteristic
255	C₂²	—	2	2	no	—
256	C₂²	—	2	2	no	—
257	C₂²	—	2	2	no	—
258	C₂²	—	2	2	no	—
259	C₂²	—	4	4	no	—
260	C₂²	—	8	2	no	—
261	C₂²	—	8	1	no	—
262	C₂²	C₂×C₁₃×#102	1	1	yes	characteristic
263	C₂²	C₁₃×#465	1	2	yes	—
264	C₄	—	2	2	no	—
265	C₄	—	8	2	no	—
266	C₄	—	8	1	no	—
267	C₄	C₁₃×#386	1	1	yes	characteristic
268	C₄	C₁₃×#416	1	1	yes	characteristic
269	C₄	C₁₃×#466	1	2	yes	—
270	C₂	—	2	2	no	—
271	C₂	—	4	2	no	—
272	C₂	—	16	1	no	—
273	C₂	C₁₃×#1893	1	1	yes	characteristic
274	C₂	C₁₃×#2143	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×#102
prime radical	C₁₃×#3050	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×M₃₂	C₂	semidirect
3. C₂×C₁₃×#359	C₂	semidirect
4. C₁₃×#1810	C₂	semidirect
5. C₁₃×#1382	C₂	semidirect
44. C₂×C₁₃×C₁₆	D₄	semidirect
52. #13064	C₁₃	direct (N × H)
90. C₂²×M₃₂	C₂×C₁₃	semidirect
92. C₂×#359	C₂×C₁₃	semidirect
93. #1810	C₂×C₁₃	semidirect
94. #1382	C₂×C₁₃	semidirect
176. C₂×C₁₆	D₄×C₁₃	semidirect
226. C₁₃	#13064	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×M₃₂	2
C₁₃×#3050	2
C₂×C₁₃×#359	2
C₁₃×#1810	2
C₁₃×#1382	2
#13064	13

Subgroups — C13×#13064 #15699403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13064 #15699403