Subgroups — C₁₃×#13009 #15699348

Order 3328.

496 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	C₂×C₁₃×#470	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#430	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#362	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#349	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1383	C₂	1	2	yes	maximal, complemented
6	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
7	C₂²×C₁₃×M₁₆	—	2	1	no	—
8	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
10	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
11	C₁₃×#470	—	2	2	no	—
12	C₁₃×#470	C₄	1	4	yes	—
13	C₁₃×#430	—	2	4	no	—
14	C₂×C₁₃×#108	—	2	1	no	—
15	C₂×C₁₃×#108	C₂²	1	2	yes	—
16	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#103	—	2	1	no	—
18	C₁₃×#362	—	2	4	no	—
19	C₁₃×#349	—	2	2	no	—
20	C₂²×Q₈×C₁₃	—	2	1	no	—
21	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
22	C₂×C₁₃×Q₁₆	—	2	2	no	—
23	C₂×C₁₃×Q₁₆	—	2	1	no	—
24	C₂×C₁₃×Q₁₆	—	2	2	no	—
25	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
26	C₂×C₁₃×M₁₆	—	2	2	no	—
27	C₂×C₁₃×M₁₆	—	2	2	no	—
28	C₂×C₁₃×M₁₆	—	2	4	no	—
29	C₂×C₁₃×M₁₆	—	2	2	no	—
30	C₂×C₁₃×M₁₆	—	4	1	no	—
31	C₂×C₁₃×M₁₆	—	4	2	no	—
32	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
33	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
34	C₂²×C₈×C₁₃	—	4	1	no	—
35	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
37	C₁₃×C₂²⋊Q₈	—	2	4	no	—
38	C₁₃×C₂²⋊Q₈	—	4	2	no	—
39	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
40	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
41	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
42	C₁₃×M₃₂	—	2	2	no	—
43	C₁₃×M₃₂	—	2	2	no	—
44	C₂×C₁₃×C₁₆	—	2	2	no	—
45	C₁₃×#108	—	2	4	no	—
46	C₁₃×#108	—	2	2	no	—
47	C₁₃×#108	D₄	1	4	yes	—
48	C₁₃×#106	—	2	1	no	—
49	C₁₃×#106	C₂×C₄	1	2	yes	—
50	C₁₃×#103	—	2	4	no	—
51	#13009	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
52	C₂⁴×C₁₃	SD₁₆	1	1	yes	characteristic
53	C₂×Q₈×C₁₃	—	2	2	no	—
54	C₂×Q₈×C₁₃	—	4	1	no	—
55	C₂×Q₈×C₁₃	—	4	1	no	—
56	C₂×Q₈×C₁₃	—	4	1	no	—
57	C₂×Q₈×C₁₃	—	4	1	no	—
58	C₂×Q₈×C₁₃	—	4	1	no	—
59	C₂²×C₄×C₁₃	—	2	1	no	—
60	C₂²×C₄×C₁₃	—	2	1	no	—
61	C₂²×C₄×C₁₃	—	2	1	no	—
62	C₂²×C₄×C₁₃	—	2	1	no	—
63	C₂²×C₄×C₁₃	—	4	1	no	—
64	C₂²×C₄×C₁₃	—	4	1	no	—
65	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
66	C₂²×C₄×C₁₃	D₈	1	2	yes	—
67	C₂²×C₄×C₁₃	SD₁₆	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
69	C₁₃×Q₁₆	—	2	4	no	—
70	C₁₃×Q₁₆	—	4	2	no	—
71	C₁₃×M₁₆	—	2	4	no	—
72	C₁₃×M₁₆	—	2	4	no	—
73	C₁₃×M₁₆	—	2	4	no	—
74	C₁₃×M₁₆	—	4	4	no	—
75	C₁₃×M₁₆	—	4	2	no	—
76	C₂×C₈×C₁₃	—	2	1	no	—
77	C₂×C₈×C₁₃	—	2	1	no	—
78	C₂×C₈×C₁₃	—	4	4	no	—
79	C₂×C₈×C₁₃	—	4	2	no	—
80	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
81	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
83	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
84	C₂×C₈×C₁₃	#41	1	2	yes	—
85	C₁₃×C₄⋊C₄	—	2	2	no	—
86	C₁₃×C₄⋊C₄	—	4	4	no	—
87	C₁₃×C₄⋊C₄	—	4	1	no	—
88	C₁₃×C₂²⋊C₄	—	4	4	no	—
89	C₁₃×C₁₆	—	4	2	no	—
90	C₂×#470	C₂×C₁₃	1	1	yes	characteristic
91	C₂×#430	C₂×C₁₃	1	1	yes	characteristic
92	C₂×#362	C₂×C₁₃	1	2	yes	complemented
93	C₂×#349	C₂×C₁₃	1	1	yes	characteristic
94	#1383	C₂×C₁₃	1	2	yes	complemented
95	C₂³×C₁₃	—	2	1	no	—
96	C₂³×C₁₃	—	2	1	no	—
97	C₂³×C₁₃	—	4	2	no	—
98	C₂³×C₁₃	#102	1	2	yes	—
99	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
100	Q₈×C₁₃	—	4	2	no	—
101	Q₈×C₁₃	—	4	2	no	—
102	Q₈×C₁₃	—	8	1	no	—
103	Q₈×C₁₃	—	8	1	no	—
104	C₂×C₄×C₁₃	—	2	1	no	—
105	C₂×C₄×C₁₃	—	2	1	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	2	no	—
110	C₂×C₄×C₁₃	—	4	2	no	—
111	C₂×C₄×C₁₃	—	4	2	no	—
112	C₂×C₄×C₁₃	—	8	2	no	—
113	C₂×C₄×C₁₃	—	8	1	no	—
114	C₂×C₄×C₁₃	—	8	1	no	—
115	C₂×C₄×C₁₃	#102	1	2	yes	—
116	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
117	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
118	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
119	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
120	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
121	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
122	C₈×C₁₃	—	2	2	no	—
123	C₈×C₁₃	—	4	4	no	—
124	C₈×C₁₃	C₄×D₄	1	2	yes	—
125	C₈×C₁₃	#121	1	2	yes	—
126	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
127	C₂²×M₁₆	—	2	1	no	—
128	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
129	C₂×C₂²⋊Q₈	—	2	1	no	—
130	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
131	#470	—	2	2	no	—
132	#470	C₄×C₁₃	1	4	yes	—
133	#430	—	2	4	no	—
134	C₂×#108	—	2	1	no	—
135	C₂×#108	C₂²×C₁₃	1	2	yes	—
136	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
137	C₂×#103	—	2	1	no	—
138	#362	—	2	4	no	—
139	#349	—	2	2	no	—
140	C₂²×C₁₃	—	2	2	no	—
141	C₂²×C₁₃	—	2	2	no	—
142	C₂²×C₁₃	—	4	2	no	—
143	C₂²×C₁₃	—	4	2	no	—
144	C₂²×C₁₃	—	8	1	no	—
145	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
146	C₂²×C₁₃	#448	1	1	yes	characteristic
147	C₂²×C₁₃	#481	1	1	yes	characteristic
148	C₄×C₁₃	—	2	2	no	—
149	C₄×C₁₃	—	8	2	no	—
150	C₄×C₁₃	—	8	2	no	—
151	C₄×C₁₃	#386	1	1	yes	characteristic
152	C₄×C₁₃	#417	1	1	yes	characteristic
153	C₄×C₁₃	#447	1	1	yes	characteristic
154	C₄×C₁₃	#480	1	1	yes	characteristic
155	C₂²×Q₈	—	2	1	no	—
156	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
157	C₂×Q₁₆	—	2	2	no	—
158	C₂×Q₁₆	—	2	1	no	—
159	C₂×Q₁₆	—	2	2	no	—
160	C₂×Q₁₆	C₂×C₄×C₁₃	1	2	yes	—
161	C₂×M₁₆	—	2	2	no	—
162	C₂×M₁₆	—	2	2	no	—
163	C₂×M₁₆	—	2	4	no	—
164	C₂×M₁₆	—	2	2	no	—
165	C₂×M₁₆	—	4	1	no	—
166	C₂×M₁₆	—	4	2	no	—
167	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
168	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
169	C₂²×C₈	—	4	1	no	—
170	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
171	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
172	C₂²⋊Q₈	—	2	4	no	—
173	C₂²⋊Q₈	—	4	2	no	—
174	C₂×C₄⋊C₄	—	2	1	no	—
175	C₂×C₄⋊C₄	—	4	1	no	—
176	C₂×C₂²⋊C₄	—	4	1	no	—
177	M₃₂	—	2	2	no	—
178	M₃₂	—	2	2	no	—
179	C₂×C₁₆	—	2	2	no	—
180	#108	—	2	4	no	—
181	#108	—	2	2	no	—
182	#108	D₄×C₁₃	1	4	yes	—
183	#106	—	2	1	no	—
184	#106	C₂×C₄×C₁₃	1	2	yes	—
185	#103	—	2	4	no	—
186	C₂×C₁₃	—	2	1	no	—
187	C₂×C₁₃	—	2	1	no	—
188	C₂×C₁₃	—	4	2	no	—
189	C₂×C₁₃	#1874	1	1	yes	characteristic
190	C₂×C₁₃	#2239	1	2	yes	—
191	C₂⁴	C₁₃×SD₁₆	1	1	yes	characteristic
192	C₂×Q₈	—	2	2	no	—
193	C₂×Q₈	—	4	1	no	—
194	C₂×Q₈	—	4	1	no	—
195	C₂×Q₈	—	4	1	no	—
196	C₂×Q₈	—	4	1	no	—
197	C₂×Q₈	—	4	1	no	—
198	C₂²×C₄	—	2	1	no	—
199	C₂²×C₄	—	2	1	no	—
200	C₂²×C₄	—	2	1	no	—
201	C₂²×C₄	—	2	1	no	—
202	C₂²×C₄	—	4	1	no	—
203	C₂²×C₄	—	4	1	no	—
204	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
205	C₂²×C₄	C₁₃×D₈	1	2	yes	—
206	C₂²×C₄	C₁₃×SD₁₆	1	1	yes	characteristic
207	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
208	Q₁₆	—	2	4	no	—
209	Q₁₆	—	4	2	no	—
210	M₁₆	—	2	4	no	—
211	M₁₆	—	2	4	no	—
212	M₁₆	—	2	4	no	—
213	M₁₆	—	4	4	no	—
214	M₁₆	—	4	2	no	—
215	C₂×C₈	—	2	1	no	—
216	C₂×C₈	—	2	1	no	—
217	C₂×C₈	—	4	4	no	—
218	C₂×C₈	—	4	2	no	—
219	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
220	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
221	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
222	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
223	C₂×C₈	C₁₃×#41	1	2	yes	—
224	C₄⋊C₄	—	2	2	no	—
225	C₄⋊C₄	—	4	4	no	—
226	C₄⋊C₄	—	4	1	no	—
227	C₂²⋊C₄	—	4	4	no	—
228	C₁₆	—	4	2	no	—
229	C₁₃	#13009	1	1	yes	characteristic, direct product factor, Sylow
230	C₂³	—	2	1	no	—
231	C₂³	—	2	1	no	—
232	C₂³	—	4	2	no	—
233	C₂³	C₁₃×#102	1	2	yes	—
234	C₂³	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
235	Q₈	—	4	2	no	—
236	Q₈	—	4	2	no	—
237	Q₈	—	8	1	no	—
238	Q₈	—	8	1	no	—
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	2	1	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	2	no	—
246	C₂×C₄	—	4	2	no	—
247	C₂×C₄	—	8	2	no	—
248	C₂×C₄	—	8	1	no	—
249	C₂×C₄	—	8	1	no	—
250	C₂×C₄	C₁₃×#102	1	2	yes	—
251	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
253	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
254	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
255	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
256	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
257	C₈	—	2	2	no	—
258	C₈	—	4	4	no	—
259	C₈	C₄×D₄×C₁₃	1	2	yes	—
260	C₈	C₁₃×#121	1	2	yes	—
261	C₂²	—	2	2	no	—
262	C₂²	—	2	2	no	—
263	C₂²	—	4	2	no	—
264	C₂²	—	4	2	no	—
265	C₂²	—	8	1	no	—
266	C₂²	C₂×C₁₃×#102	1	1	yes	characteristic
267	C₂²	C₁₃×#448	1	1	yes	characteristic
268	C₂²	C₁₃×#481	1	1	yes	characteristic
269	C₄	—	2	2	no	—
270	C₄	—	8	2	no	—
271	C₄	—	8	2	no	—
272	C₄	C₁₃×#386	1	1	yes	characteristic
273	C₄	C₁₃×#417	1	1	yes	characteristic
274	C₄	C₁₃×#447	1	1	yes	characteristic
275	C₄	C₁₃×#480	1	1	yes	characteristic
276	C₂	—	2	1	no	—
277	C₂	—	2	1	no	—
278	C₂	—	4	2	no	—
279	C₂	C₁₃×#1874	1	1	yes	characteristic
280	C₂	C₁₃×#2239	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	#481
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂⁴×C₁₃	SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂²×C₁₃×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₃×#362	C₂	semidirect
5. C₁₃×#1383	C₂	semidirect
51. #13009	C₁₃	direct (N × H)
92. C₂×#362	C₂×C₁₃	semidirect
94. #1383	C₂×C₁₃	semidirect
229. C₁₃	#13009	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×#470	2
C₂×C₁₃×#430	2
C₂×C₁₃×#362	2
C₂×C₁₃×#349	2
C₁₃×#1383	2
#13009	13

Subgroups — C13×#13009 #15699348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13009 #15699348