Subgroups — C₁₃×#10262 #15696601

Order 3328.

742 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#493	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#460	C₂	1	2	yes	maximal, complemented
3	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#331	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1277	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₁₃×SD₁₆	—	2	2	no	—
7	C₂²×C₁₃×D₈	—	2	2	no	—
8	C₂×C₁₃×#127	C₂²	1	2	yes	—
9	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₁₃×#493	—	2	4	no	—
11	C₁₃×#460	—	2	4	no	—
12	C₁₃×#460	—	2	4	no	—
13	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₃×#102	—	2	2	no	—
16	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#336	—	2	2	no	—
18	C₁₃×#331	—	2	4	no	—
19	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
20	C₂²×D₄×C₁₃	—	2	2	no	—
21	C₂²×D₄×C₁₃	—	2	2	no	—
22	C₂²×D₄×C₁₃	—	2	2	no	—
23	C₂×C₁₃×SD₁₆	—	2	8	no	—
24	C₂×C₁₃×SD₁₆	—	4	4	no	—
25	C₂×C₁₃×SD₁₆	—	4	4	no	—
26	C₂×C₁₃×D₈	—	2	8	no	—
27	C₂×C₁₃×D₈	—	4	4	no	—
28	C₂×C₁₃×D₈	—	4	4	no	—
29	C₂²×C₈×C₁₃	—	2	2	no	—
30	C₂²×C₈×C₁₃	—	2	1	no	—
31	C₂²×C₈×C₁₃	D₄	1	2	yes	—
32	C₁₃×#127	—	2	2	no	—
33	C₁₃×#127	—	2	2	no	—
34	C₁₃×#127	—	2	2	no	—
35	C₁₃×#127	D₄	1	4	yes	—
36	C₄×Q₈×C₁₃	—	2	2	no	—
37	C₄×Q₈×C₁₃	—	2	2	no	—
38	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
39	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₃	—	2	1	no	—
41	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
42	C₁₃×C₄⋊C₈	—	2	2	no	—
43	C₁₃×C₄⋊C₈	—	2	2	no	—
44	C₁₃×C₄⋊C₈	D₄	1	4	yes	—
45	C₁₃×#102	—	2	8	no	—
46	C₄×C₈×C₁₃	—	2	2	no	—
47	#10262	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂⁴×C₁₃	—	4	2	no	—
49	C₂×Q₈×C₁₃	—	2	1	no	—
50	C₂×Q₈×C₁₃	—	2	2	no	—
51	C₂×Q₈×C₁₃	—	2	2	no	—
52	C₂×Q₈×C₁₃	D₈	1	2	yes	complemented
53	C₂×D₄×C₁₃	—	2	4	no	—
54	C₂×D₄×C₁₃	—	2	4	no	—
55	C₂×D₄×C₁₃	—	2	4	no	—
56	C₂×D₄×C₁₃	—	4	2	no	—
57	C₂×D₄×C₁₃	—	4	2	no	—
58	C₂×D₄×C₁₃	—	4	2	no	—
59	C₂×D₄×C₁₃	—	4	2	no	—
60	C₂×D₄×C₁₃	—	4	4	no	—
61	C₂×D₄×C₁₃	—	4	2	no	—
62	C₂×D₄×C₁₃	—	4	4	no	—
63	C₂×D₄×C₁₃	—	4	2	no	—
64	C₂×D₄×C₁₃	—	4	2	no	—
65	C₂×D₄×C₁₃	—	8	4	no	—
66	C₂²×C₄×C₁₃	—	2	1	no	—
67	C₂²×C₄×C₁₃	—	2	1	no	—
68	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
71	C₁₃×SD₁₆	—	4	16	no	—
72	C₁₃×D₈	—	4	16	no	—
73	C₂×C₈×C₁₃	—	2	2	no	—
74	C₂×C₈×C₁₃	—	2	2	no	—
75	C₂×C₈×C₁₃	—	2	4	no	—
76	C₂×C₈×C₁₃	—	4	2	no	—
77	C₂×C₈×C₁₃	—	4	2	no	—
78	C₂×C₈×C₁₃	—	4	1	no	—
79	C₂×C₈×C₁₃	—	4	2	no	—
80	C₂×C₈×C₁₃	SD₁₆	1	4	yes	complemented
81	C₁₃×C₄⋊C₄	—	2	2	no	—
82	C₁₃×C₄⋊C₄	—	4	2	no	—
83	C₄²×C₁₃	—	4	1	no	—
84	C₄²×C₁₃	—	4	1	no	—
85	C₄²×C₁₃	C₂×D₄	1	2	yes	—
86	C₄²×C₁₃	C₂×D₄	1	2	yes	—
87	C₂×#493	C₂×C₁₃	1	1	yes	characteristic
88	C₂×#460	C₂×C₁₃	1	2	yes	complemented
89	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
90	C₂×#331	C₂×C₁₃	1	2	yes	complemented
91	#1277	C₂×C₁₃	1	1	yes	characteristic, complemented
92	C₂³×C₁₃	—	4	4	no	—
93	C₂³×C₁₃	—	8	4	no	—
94	C₂³×C₁₃	—	8	2	no	—
95	C₂³×C₁₃	—	8	2	no	—
96	C₂³×C₁₃	—	8	4	no	—
97	C₂³×C₁₃	#121	1	1	yes	characteristic
98	Q₈×C₁₃	—	2	4	no	—
99	Q₈×C₁₃	—	4	2	no	—
100	D₄×C₁₃	—	4	4	no	—
101	D₄×C₁₃	—	4	4	no	—
102	D₄×C₁₃	—	4	8	no	—
103	D₄×C₁₃	—	8	4	no	—
104	D₄×C₁₃	—	8	4	no	—
105	D₄×C₁₃	—	8	2	no	—
106	D₄×C₁₃	—	8	2	no	—
107	D₄×C₁₃	—	8	2	no	—
108	D₄×C₁₃	—	8	2	no	—
109	C₂×C₄×C₁₃	—	2	2	no	—
110	C₂×C₄×C₁₃	—	2	2	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	#120	1	2	yes	—
116	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
117	C₂×C₄×C₁₃	#121	1	2	yes	—
118	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
119	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
120	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
121	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
122	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
123	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
124	C₈×C₁₃	—	2	4	no	—
125	C₈×C₁₃	—	4	4	no	—
126	C₈×C₁₃	—	8	1	no	—
127	C₂²×SD₁₆	—	2	2	no	—
128	C₂²×D₈	—	2	2	no	—
129	C₂×#127	C₂²×C₁₃	1	2	yes	—
130	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
131	#493	—	2	4	no	—
132	#460	—	2	4	no	—
133	#460	—	2	4	no	—
134	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
135	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
136	C₂×#102	—	2	2	no	—
137	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
138	#336	—	2	2	no	—
139	#331	—	2	4	no	—
140	C₂²×C₁₃	—	8	4	no	—
141	C₂²×C₁₃	—	8	4	no	—
142	C₂²×C₁₃	—	8	4	no	—
143	C₂²×C₁₃	—	16	4	no	—
144	C₂²×C₁₃	—	16	4	no	—
145	C₂²×C₁₃	#392	1	1	yes	characteristic
146	C₂²×C₁₃	#460	1	2	yes	—
147	C₂²×C₁₃	#466	1	1	yes	characteristic
148	C₂²×C₁₃	#469	1	1	yes	characteristic
149	C₂²×C₁₃	#472	1	2	yes	—
150	C₄×C₁₃	—	2	2	no	—
151	C₄×C₁₃	—	4	2	no	—
152	C₄×C₁₃	—	8	1	no	—
153	C₄×C₁₃	#447	1	2	yes	—
154	C₄×C₁₃	#449	1	2	yes	—
155	C₄×C₁₃	#450	1	2	yes	—
156	C₄×C₁₃	#492	1	1	yes	characteristic
157	C₄×C₁₃	#496	1	1	yes	characteristic
158	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
159	C₂²×D₄	—	2	2	no	—
160	C₂²×D₄	—	2	2	no	—
161	C₂²×D₄	—	2	2	no	—
162	C₂×SD₁₆	—	2	8	no	—
163	C₂×SD₁₆	—	4	4	no	—
164	C₂×SD₁₆	—	4	4	no	—
165	C₂×D₈	—	2	8	no	—
166	C₂×D₈	—	4	4	no	—
167	C₂×D₈	—	4	4	no	—
168	C₂²×C₈	—	2	2	no	—
169	C₂²×C₈	—	2	1	no	—
170	C₂²×C₈	D₄×C₁₃	1	2	yes	—
171	#127	—	2	2	no	—
172	#127	—	2	2	no	—
173	#127	—	2	2	no	—
174	#127	D₄×C₁₃	1	4	yes	—
175	C₄×Q₈	—	2	2	no	—
176	C₄×Q₈	—	2	2	no	—
177	C₂×C₄⋊C₄	—	2	1	no	—
178	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
179	C₂×C₄²	—	2	1	no	—
180	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
181	C₄⋊C₈	—	2	2	no	—
182	C₄⋊C₈	—	2	2	no	—
183	C₄⋊C₈	D₄×C₁₃	1	4	yes	—
184	#102	—	2	8	no	—
185	C₄×C₈	—	2	2	no	—
186	C₂×C₁₃	—	16	4	no	—
187	C₂×C₁₃	#1668	1	2	yes	—
188	C₂×C₁₃	#1688	1	2	yes	—
189	C₂×C₁₃	#1999	1	1	yes	characteristic
190	C₂×C₁₃	#2014	1	1	yes	characteristic
191	C₂×C₁₃	#2018	1	1	yes	characteristic
192	C₂⁴	—	4	2	no	—
193	C₂×Q₈	—	2	1	no	—
194	C₂×Q₈	—	2	2	no	—
195	C₂×Q₈	—	2	2	no	—
196	C₂×Q₈	C₁₃×D₈	1	2	yes	complemented
197	C₂×D₄	—	2	4	no	—
198	C₂×D₄	—	2	4	no	—
199	C₂×D₄	—	2	4	no	—
200	C₂×D₄	—	4	2	no	—
201	C₂×D₄	—	4	2	no	—
202	C₂×D₄	—	4	2	no	—
203	C₂×D₄	—	4	2	no	—
204	C₂×D₄	—	4	4	no	—
205	C₂×D₄	—	4	2	no	—
206	C₂×D₄	—	4	4	no	—
207	C₂×D₄	—	4	2	no	—
208	C₂×D₄	—	4	2	no	—
209	C₂×D₄	—	8	4	no	—
210	C₂²×C₄	—	2	1	no	—
211	C₂²×C₄	—	2	1	no	—
212	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
213	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
214	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
215	SD₁₆	—	4	16	no	—
216	D₈	—	4	16	no	—
217	C₂×C₈	—	2	2	no	—
218	C₂×C₈	—	2	2	no	—
219	C₂×C₈	—	2	4	no	—
220	C₂×C₈	—	4	2	no	—
221	C₂×C₈	—	4	2	no	—
222	C₂×C₈	—	4	1	no	—
223	C₂×C₈	—	4	2	no	—
224	C₂×C₈	C₁₃×SD₁₆	1	4	yes	complemented
225	C₄⋊C₄	—	2	2	no	—
226	C₄⋊C₄	—	4	2	no	—
227	C₄²	—	4	1	no	—
228	C₄²	—	4	1	no	—
229	C₄²	C₂×D₄×C₁₃	1	2	yes	—
230	C₄²	C₂×D₄×C₁₃	1	2	yes	—
231	C₁₃	#10262	1	1	yes	characteristic, direct product factor, Sylow
232	C₂³	—	4	4	no	—
233	C₂³	—	8	4	no	—
234	C₂³	—	8	2	no	—
235	C₂³	—	8	2	no	—
236	C₂³	—	8	4	no	—
237	C₂³	C₁₃×#121	1	1	yes	characteristic
238	Q₈	—	2	4	no	—
239	Q₈	—	4	2	no	—
240	D₄	—	4	4	no	—
241	D₄	—	4	4	no	—
242	D₄	—	4	8	no	—
243	D₄	—	8	4	no	—
244	D₄	—	8	4	no	—
245	D₄	—	8	2	no	—
246	D₄	—	8	2	no	—
247	D₄	—	8	2	no	—
248	D₄	—	8	2	no	—
249	C₂×C₄	—	2	2	no	—
250	C₂×C₄	—	2	2	no	—
251	C₂×C₄	—	4	1	no	—
252	C₂×C₄	—	4	1	no	—
253	C₂×C₄	—	4	1	no	—
254	C₂×C₄	—	4	2	no	—
255	C₂×C₄	C₁₃×#120	1	2	yes	—
256	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
257	C₂×C₄	C₁₃×#121	1	2	yes	—
258	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
259	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
260	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
261	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
262	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
263	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
264	C₈	—	2	4	no	—
265	C₈	—	4	4	no	—
266	C₈	—	8	1	no	—
267	C₂²	—	8	4	no	—
268	C₂²	—	8	4	no	—
269	C₂²	—	8	4	no	—
270	C₂²	—	16	4	no	—
271	C₂²	—	16	4	no	—
272	C₂²	C₁₃×#392	1	1	yes	characteristic
273	C₂²	C₁₃×#460	1	2	yes	—
274	C₂²	C₁₃×#466	1	1	yes	characteristic
275	C₂²	C₁₃×#469	1	1	yes	characteristic
276	C₂²	C₁₃×#472	1	2	yes	—
277	C₄	—	2	2	no	—
278	C₄	—	4	2	no	—
279	C₄	—	8	1	no	—
280	C₄	C₁₃×#447	1	2	yes	—
281	C₄	C₁₃×#449	1	2	yes	—
282	C₄	C₁₃×#450	1	2	yes	—
283	C₄	C₁₃×#492	1	1	yes	characteristic
284	C₄	C₁₃×#496	1	1	yes	characteristic
285	C₂	—	16	4	no	—
286	C₂	C₁₃×#1668	1	2	yes	—
287	C₂	C₁₃×#1688	1	2	yes	—
288	C₂	C₁₃×#1999	1	1	yes	characteristic
289	C₂	C₁₃×#2014	1	1	yes	characteristic
290	C₂	C₁₃×#2018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#493	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#460	C₂	semidirect
3. C₁₃×#1984	C₂	semidirect
4. C₂×C₁₃×#331	C₂	semidirect
5. C₁₃×#1277	C₂	semidirect
47. #10262	C₁₃	direct (N × H)
52. C₂×Q₈×C₁₃	D₈	semidirect
80. C₂×C₈×C₁₃	SD₁₆	semidirect
88. C₂×#460	C₂×C₁₃	semidirect
89. #1984	C₂×C₁₃	semidirect
90. C₂×#331	C₂×C₁₃	semidirect
91. #1277	C₂×C₁₃	semidirect
196. C₂×Q₈	C₁₃×D₈	semidirect
224. C₂×C₈	C₁₃×SD₁₆	semidirect
231. C₁₃	#10262	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×C₁₃×#493	2
C₂×C₁₃×#460	2
C₁₃×#1984	2
C₂×C₁₃×#331	2
C₁₃×#1277	2
#10262	13

Subgroups — C13×#10262 #15696601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10262 #15696601