Subgroups — C₁₃×#12807 #15699146

Order 3328.

428 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2126	C₂	1	2	yes	maximal
3	C₁₃×#1812	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1391	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#131	C₄	1	1	yes	characteristic, complemented
6	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
7	C₁₃×#532	C₂²	1	1	yes	characteristic
8	C₁₃×#436	—	2	2	no	—
9	C₈×D₄×C₁₃	—	2	2	no	—
10	C₁₃×#427	—	2	2	no	—
11	C₁₃×#423	C₄	1	1	yes	characteristic, complemented
12	C₁₃×#410	C₂²	1	4	yes	—
13	C₁₃×#408	C₄	1	1	yes	characteristic, complemented
14	C₁₃×#408	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic, complemented
16	C₁₃×#354	—	2	2	no	—
17	C₁₃×#353	—	2	2	no	—
18	C₁₃×H(3,ℤ/4)	—	2	2	no	—
19	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
20	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
21	C₁₃×#131	—	4	1	no	—
22	C₁₃×#131	—	4	1	no	—
23	C₁₃×#131	—	4	1	no	—
24	C₁₃×#131	—	4	1	no	—
25	C₂×C₁₃×M₁₆	—	2	1	no	—
26	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
27	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
28	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
29	C₂²×C₈×C₁₃	—	2	1	no	—
30	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₃	D₄	1	2	yes	—
33	C₁₃×C₄⋊Q₈	Q₈	1	1	yes	characteristic
34	C₁₃×#127	D₄	1	1	yes	characteristic
35	C₁₃×#124	D₄	1	1	yes	characteristic
36	C₁₃×#124	Q₈	1	1	yes	characteristic
37	C₁₃×#121	—	2	2	no	—
38	C₄×D₄×C₁₃	—	2	2	no	—
39	C₁₃×#117	—	2	4	no	—
40	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₁₃×#107	—	4	2	no	—
42	C₁₃×#106	—	4	2	no	—
43	C₁₃×C₄⋊C₈	—	2	2	no	—
44	C₁₃×#99	—	2	4	no	—
45	C₁₃×#99	—	2	4	no	—
46	C₁₃×C₂²⋊C₈	—	2	2	no	—
47	C₁₃×C₂²⋊C₈	—	2	2	no	—
48	C₄×C₈×C₁₃	—	2	1	no	—
49	C₄×C₈×C₁₃	—	2	1	no	—
50	#12807	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₁₃×#41	—	4	1	no	—
52	C₁₃×#41	—	4	1	no	—
53	C₁₃×#41	—	4	1	no	—
54	C₁₃×#41	—	4	1	no	—
55	C₂×Q₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
56	C₂×Q₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
57	C₂×D₄×C₁₃	—	2	1	no	—
58	C₂×D₄×C₁₃	—	2	2	no	—
59	C₂×D₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
60	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
61	C₂×D₄×C₁₃	#41	1	2	yes	—
62	C₂²×C₄×C₁₃	—	2	1	no	—
63	C₂²×C₄×C₁₃	—	2	1	no	—
64	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
66	C₁₃×M₁₆	—	4	1	no	—
67	C₁₃×M₁₆	—	4	2	no	—
68	C₁₃×M₁₆	—	4	2	no	—
69	C₁₃×M₁₆	—	4	1	no	—
70	C₂×C₈×C₁₃	—	2	2	no	—
71	C₂×C₈×C₁₃	—	2	2	no	—
72	C₂×C₈×C₁₃	—	2	1	no	—
73	C₂×C₈×C₁₃	—	2	1	no	—
74	C₂×C₈×C₁₃	—	2	1	no	—
75	C₂×C₈×C₁₃	—	2	1	no	—
76	C₂×C₈×C₁₃	—	4	1	no	—
77	C₂×C₈×C₁₃	—	4	1	no	—
78	C₂×C₈×C₁₃	—	4	1	no	—
79	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
80	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₁₃×C₄⋊C₄	—	2	2	no	—
83	C₁₃×C₄⋊C₄	—	4	4	no	—
84	C₁₃×C₂²⋊C₄	—	2	2	no	—
85	C₁₃×C₂²⋊C₄	—	2	2	no	—
86	C₁₃×C₂²⋊C₄	—	4	4	no	—
87	C₄²×C₁₃	—	2	1	no	—
88	C₄²×C₁₃	—	4	4	no	—
89	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
90	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
91	#2931	C₂×C₁₃	1	1	yes	characteristic
92	#2126	C₂×C₁₃	1	2	yes	—
93	#1812	C₂×C₁₃	1	2	yes	complemented
94	#1391	C₂×C₁₃	1	2	yes	complemented
95	C₂³×C₁₃	—	2	1	no	—
96	C₂³×C₁₃	#117	1	1	yes	characteristic
97	C₂³×C₁₃	#121	1	2	yes	—
98	Q₈×C₁₃	—	4	1	no	—
99	Q₈×C₁₃	—	4	1	no	—
100	D₄×C₁₃	—	4	1	no	—
101	D₄×C₁₃	—	4	2	no	—
102	D₄×C₁₃	—	4	4	no	—
103	D₄×C₁₃	—	4	1	no	—
104	D₄×C₁₃	—	4	2	no	—
105	C₂×C₄×C₁₃	—	2	1	no	—
106	C₂×C₄×C₁₃	—	2	2	no	—
107	C₂×C₄×C₁₃	—	2	1	no	—
108	C₂×C₄×C₁₃	—	2	2	no	—
109	C₂×C₄×C₁₃	—	2	1	no	—
110	C₂×C₄×C₁₃	—	2	1	no	—
111	C₂×C₄×C₁₃	—	2	1	no	—
112	C₂×C₄×C₁₃	—	4	2	no	—
113	C₂×C₄×C₁₃	—	4	1	no	—
114	C₂×C₄×C₁₃	—	4	1	no	—
115	C₂×C₄×C₁₃	—	8	4	no	—
116	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
117	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
119	C₈×C₁₃	—	2	2	no	—
120	C₈×C₁₃	—	2	1	no	—
121	C₈×C₁₃	—	4	1	no	—
122	C₈×C₁₃	—	4	1	no	—
123	C₈×C₁₃	#99	1	1	yes	characteristic
124	C₈×C₁₃	#99	1	1	yes	characteristic
125	C₂×#131	C₄×C₁₃	1	1	yes	characteristic, complemented
126	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
127	#532	C₂²×C₁₃	1	1	yes	characteristic
128	#436	—	2	2	no	—
129	C₈×D₄	—	2	2	no	—
130	#427	—	2	2	no	—
131	#423	C₄×C₁₃	1	1	yes	characteristic, complemented
132	#410	C₂²×C₁₃	1	4	yes	—
133	#408	C₄×C₁₃	1	1	yes	characteristic, complemented
134	#408	C₂²×C₁₃	1	1	yes	characteristic
135	C₂×C₄×C₈	C₄×C₁₃	1	1	yes	characteristic, complemented
136	#354	—	2	2	no	—
137	#353	—	2	2	no	—
138	H(3,ℤ/4)	—	2	2	no	—
139	C₂²×C₁₃	—	2	2	no	—
140	C₂²×C₁₃	—	2	1	no	—
141	C₂²×C₁₃	—	4	1	no	—
142	C₂²×C₁₃	—	4	2	no	—
143	C₂²×C₁₃	—	4	2	no	—
144	C₂²×C₁₃	—	4	1	no	—
145	C₂²×C₁₃	#380	1	1	yes	characteristic
146	C₄×C₁₃	—	2	2	no	—
147	C₄×C₁₃	—	2	1	no	—
148	C₄×C₁₃	—	2	2	no	—
149	C₄×C₁₃	—	4	1	no	—
150	C₄×C₁₃	—	4	1	no	—
151	C₄×C₁₃	—	16	4	no	—
152	C₄×C₁₃	C₂×#99	1	1	yes	characteristic
153	C₄×C₁₃	#410	1	1	yes	characteristic
154	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
155	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
156	#131	—	4	1	no	—
157	#131	—	4	1	no	—
158	#131	—	4	1	no	—
159	#131	—	4	1	no	—
160	C₂×M₁₆	—	2	1	no	—
161	C₂×M₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
162	C₂×M₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
163	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
164	C₂²×C₈	—	2	1	no	—
165	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
166	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
167	C₂²×C₈	D₄×C₁₃	1	2	yes	—
168	C₄⋊Q₈	Q₈×C₁₃	1	1	yes	characteristic
169	#127	D₄×C₁₃	1	1	yes	characteristic
170	#124	D₄×C₁₃	1	1	yes	characteristic
171	#124	Q₈×C₁₃	1	1	yes	characteristic
172	#121	—	2	2	no	—
173	C₄×D₄	—	2	2	no	—
174	#117	—	2	4	no	—
175	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
176	#107	—	4	2	no	—
177	#106	—	4	2	no	—
178	C₄⋊C₈	—	2	2	no	—
179	#99	—	2	4	no	—
180	#99	—	2	4	no	—
181	C₂²⋊C₈	—	2	2	no	—
182	C₂²⋊C₈	—	2	2	no	—
183	C₄×C₈	—	2	1	no	—
184	C₄×C₈	—	2	1	no	—
185	C₂×C₁₃	—	2	1	no	—
186	C₂×C₁₃	—	4	2	no	—
187	C₂×C₁₃	—	4	1	no	—
188	C₂×C₁₃	—	8	1	no	—
189	C₂×C₁₃	#1799	1	1	yes	characteristic
190	#41	—	4	1	no	—
191	#41	—	4	1	no	—
192	#41	—	4	1	no	—
193	#41	—	4	1	no	—
194	C₂×Q₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
195	C₂×Q₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
196	C₂×D₄	—	2	1	no	—
197	C₂×D₄	—	2	2	no	—
198	C₂×D₄	C₁₃×C₄⋊C₄	1	1	yes	characteristic
199	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
200	C₂×D₄	C₁₃×#41	1	2	yes	—
201	C₂²×C₄	—	2	1	no	—
202	C₂²×C₄	—	2	1	no	—
203	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
204	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
205	M₁₆	—	4	1	no	—
206	M₁₆	—	4	2	no	—
207	M₁₆	—	4	2	no	—
208	M₁₆	—	4	1	no	—
209	C₂×C₈	—	2	2	no	—
210	C₂×C₈	—	2	2	no	—
211	C₂×C₈	—	2	1	no	—
212	C₂×C₈	—	2	1	no	—
213	C₂×C₈	—	2	1	no	—
214	C₂×C₈	—	2	1	no	—
215	C₂×C₈	—	4	1	no	—
216	C₂×C₈	—	4	1	no	—
217	C₂×C₈	—	4	1	no	—
218	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
220	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
221	C₄⋊C₄	—	2	2	no	—
222	C₄⋊C₄	—	4	4	no	—
223	C₂²⋊C₄	—	2	2	no	—
224	C₂²⋊C₄	—	2	2	no	—
225	C₂²⋊C₄	—	4	4	no	—
226	C₄²	—	2	1	no	—
227	C₄²	—	4	4	no	—
228	C₄²	C₁₃×C₄⋊C₄	1	1	yes	characteristic
229	C₄²	C₁₃×C₄⋊C₄	1	1	yes	characteristic
230	C₁₃	#12807	1	1	yes	characteristic, direct product factor, Sylow
231	C₂³	—	2	1	no	—
232	C₂³	C₁₃×#117	1	1	yes	characteristic
233	C₂³	C₁₃×#121	1	2	yes	—
234	Q₈	—	4	1	no	—
235	Q₈	—	4	1	no	—
236	D₄	—	4	1	no	—
237	D₄	—	4	2	no	—
238	D₄	—	4	1	no	—
239	D₄	—	4	4	no	—
240	D₄	—	4	2	no	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	2	1	no	—
244	C₂×C₄	—	2	2	no	—
245	C₂×C₄	—	2	1	no	—
246	C₂×C₄	—	2	1	no	—
247	C₂×C₄	—	2	1	no	—
248	C₂×C₄	—	4	2	no	—
249	C₂×C₄	—	4	1	no	—
250	C₂×C₄	—	4	1	no	—
251	C₂×C₄	—	8	4	no	—
252	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
254	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
255	C₈	—	2	2	no	—
256	C₈	—	2	1	no	—
257	C₈	—	4	1	no	—
258	C₈	—	4	1	no	—
259	C₈	C₁₃×#99	1	1	yes	characteristic
260	C₈	C₁₃×#99	1	1	yes	characteristic
261	C₂²	—	2	2	no	—
262	C₂²	—	2	1	no	—
263	C₂²	—	4	1	no	—
264	C₂²	—	4	2	no	—
265	C₂²	—	4	2	no	—
266	C₂²	—	4	1	no	—
267	C₂²	C₁₃×#380	1	1	yes	characteristic
268	C₄	—	2	2	no	—
269	C₄	—	2	1	no	—
270	C₄	—	2	2	no	—
271	C₄	—	4	1	no	—
272	C₄	—	4	1	no	—
273	C₄	—	16	4	no	—
274	C₄	C₂×C₁₃×#99	1	1	yes	characteristic
275	C₄	C₁₃×#410	1	1	yes	characteristic
276	C₂	—	2	1	no	—
277	C₂	—	4	2	no	—
278	C₂	—	4	1	no	—
279	C₂	—	8	1	no	—
280	C₂	C₁₃×#1799	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	#410
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×#41	C₂³×C₁₃
socle	C₂×C₁₃	#1799
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂×C₈×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#1812	C₂	semidirect
4. C₁₃×#1391	C₂	semidirect
5. C₂×C₁₃×#131	C₄	semidirect
11. C₁₃×#423	C₄	semidirect
13. C₁₃×#408	C₄	semidirect
15. C₂×C₄×C₈×C₁₃	C₄	semidirect
50. #12807	C₁₃	direct (N × H)
93. #1812	C₂×C₁₃	semidirect
94. #1391	C₂×C₁₃	semidirect
125. C₂×#131	C₄×C₁₃	semidirect
131. #423	C₄×C₁₃	semidirect
133. #408	C₄×C₁₃	semidirect
135. C₂×C₄×C₈	C₄×C₁₃	semidirect
230. C₁₃	#12807	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×#2931	2
C₁₃×#2126	2
C₁₃×#1812	2
C₁₃×#1391	2
#12807	13

Subgroups — C13×#12807 #15699146

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12807 #15699146