Subgroups — C₁₃×#8279 #15694618

Order 3328.

394 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#1767	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1744	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#335	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#334	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1277	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1277	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#97	—	2	1	no	—
13	C₂×C₄×C₈×C₁₃	—	2	1	no	—
14	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₄³×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#336	—	2	1	no	—
18	C₁₃×#336	—	2	1	no	—
19	C₁₃×#336	C₄	1	4	yes	—
20	C₁₃×#335	C₄	1	4	yes	complemented
21	C₁₃×#334	C₄	1	4	yes	complemented
22	C₂²×C₈×C₁₃	—	2	1	no	—
23	C₂²×C₈×C₁₃	—	2	1	no	—
24	C₂²×C₈×C₁₃	—	2	1	no	—
25	C₂²×C₈×C₁₃	—	2	1	no	—
26	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
27	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
30	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
32	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
33	C₁₃×C₄⋊C₈	—	2	1	no	—
34	C₁₃×C₄⋊C₈	—	2	1	no	—
35	C₁₃×C₄⋊C₈	—	2	1	no	—
36	C₁₃×C₄⋊C₈	—	2	1	no	—
37	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
38	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
39	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
40	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
41	C₁₃×#97	—	4	2	no	—
42	C₄×C₈×C₁₃	—	2	1	no	—
43	C₄×C₈×C₁₃	—	2	1	no	—
44	C₄×C₈×C₁₃	—	4	2	no	—
45	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
46	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
47	#8279	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
50	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
53	C₂×C₈×C₁₃	—	2	4	no	—
54	C₂×C₈×C₁₃	—	2	2	no	—
55	C₂×C₈×C₁₃	—	2	2	no	—
56	C₂×C₈×C₁₃	—	2	2	no	—
57	C₂×C₈×C₁₃	—	2	2	no	—
58	C₂×C₈×C₁₃	—	2	2	no	—
59	C₂×C₈×C₁₃	—	2	4	no	—
60	C₂×C₈×C₁₃	—	4	1	no	—
61	C₂×C₈×C₁₃	—	4	1	no	—
62	C₂×C₈×C₁₃	—	4	1	no	—
63	C₂×C₈×C₁₃	—	4	1	no	—
64	C₂×C₈×C₁₃	—	4	1	no	—
65	C₂×C₈×C₁₃	—	4	1	no	—
66	C₂×C₈×C₁₃	—	4	1	no	—
67	C₂×C₈×C₁₃	—	4	1	no	—
68	C₂×C₈×C₁₃	C₄²	1	4	yes	—
69	C₄²×C₁₃	—	2	4	no	—
70	C₄²×C₁₃	—	2	4	no	—
71	C₄²×C₁₃	—	2	1	no	—
72	C₄²×C₁₃	—	2	1	no	—
73	C₄²×C₁₃	—	2	1	no	—
74	C₄²×C₁₃	—	2	1	no	—
75	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
76	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
77	C₄²×C₁₃	#41	1	1	yes	characteristic
78	C₄²×C₁₃	#41	1	1	yes	characteristic
79	#1767	C₂×C₁₃	1	1	yes	characteristic
80	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
81	#1744	C₂×C₁₃	1	1	yes	characteristic
82	C₂×#335	C₂×C₁₃	1	1	yes	characteristic
83	C₂×#334	C₂×C₁₃	1	1	yes	characteristic
84	#1277	C₂×C₁₃	1	1	yes	characteristic
85	#1277	C₂×C₁₃	1	1	yes	characteristic
86	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₁₃	—	2	2	no	—
88	C₂×C₄×C₁₃	—	2	2	no	—
89	C₂×C₄×C₁₃	—	2	2	no	—
90	C₂×C₄×C₁₃	—	2	2	no	—
91	C₂×C₄×C₁₃	—	2	2	no	—
92	C₂×C₄×C₁₃	—	2	2	no	—
93	C₂×C₄×C₁₃	#108	1	4	yes	—
94	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
95	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
96	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
97	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
98	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
99	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
100	C₂×C₄×C₁₃	#131	1	4	yes	—
101	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
102	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
103	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
104	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
105	C₈×C₁₃	—	2	4	no	—
106	C₈×C₁₃	—	4	2	no	—
107	C₈×C₁₃	—	4	2	no	—
108	C₈×C₁₃	—	4	2	no	—
109	C₈×C₁₃	—	4	2	no	—
110	C₈×C₁₃	—	4	2	no	—
111	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
112	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
113	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
114	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
115	C₂×#97	—	2	1	no	—
116	C₂×C₄×C₈	—	2	1	no	—
117	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
118	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
119	C₄³	C₂²×C₁₃	1	1	yes	characteristic
120	#336	—	2	1	no	—
121	#336	—	2	1	no	—
122	#336	C₄×C₁₃	1	4	yes	—
123	#335	C₄×C₁₃	1	4	yes	complemented
124	#334	C₄×C₁₃	1	4	yes	complemented
125	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
126	C₂²×C₁₃	#424	1	2	yes	—
127	C₂²×C₁₃	#428	1	1	yes	characteristic
128	C₂²×C₁₃	#428	1	1	yes	characteristic
129	C₂²×C₁₃	C₂×#108	1	2	yes	—
130	C₄×C₁₃	—	2	4	no	—
131	C₄×C₁₃	—	2	1	no	—
132	C₄×C₁₃	—	2	1	no	—
133	C₄×C₁₃	—	4	2	no	—
134	C₄×C₁₃	#405	1	2	yes	—
135	C₄×C₁₃	#433	1	2	yes	—
136	C₄×C₁₃	#440	1	1	yes	characteristic
137	C₄×C₁₃	#440	1	1	yes	characteristic
138	C₄×C₁₃	#441	1	1	yes	characteristic
139	C₄×C₁₃	#442	1	1	yes	characteristic
140	C₂²×C₈	—	2	1	no	—
141	C₂²×C₈	—	2	1	no	—
142	C₂²×C₈	—	2	1	no	—
143	C₂²×C₈	—	2	1	no	—
144	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
145	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
146	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
147	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
148	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
149	C₂×C₄²	Q₈×C₁₃	1	2	yes	—
150	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
151	C₄⋊C₈	—	2	1	no	—
152	C₄⋊C₈	—	2	1	no	—
153	C₄⋊C₈	—	2	1	no	—
154	C₄⋊C₈	—	2	1	no	—
155	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
156	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
157	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
158	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
159	#97	—	4	2	no	—
160	C₄×C₈	—	2	1	no	—
161	C₄×C₈	—	2	1	no	—
162	C₄×C₈	—	4	2	no	—
163	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
164	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
165	C₂×C₁₃	#1573	1	2	yes	—
166	C₂×C₁₃	#1574	1	2	yes	—
167	C₂×C₁₃	#1768	1	1	yes	characteristic
168	C₂×C₁₃	#1776	1	1	yes	characteristic
169	C₂×C₁₃	C₄×#108	1	1	yes	characteristic
170	C₂²×C₄	C₁₃×C₄⋊C₄	1	2	yes	—
171	C₂²×C₄	C₁₃×C₄⋊C₄	1	2	yes	—
172	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
173	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
174	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
175	C₂×C₈	—	2	4	no	—
176	C₂×C₈	—	2	2	no	—
177	C₂×C₈	—	2	2	no	—
178	C₂×C₈	—	2	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	2	4	no	—
182	C₂×C₈	—	4	1	no	—
183	C₂×C₈	—	4	1	no	—
184	C₂×C₈	—	4	1	no	—
185	C₂×C₈	—	4	1	no	—
186	C₂×C₈	—	4	1	no	—
187	C₂×C₈	—	4	1	no	—
188	C₂×C₈	—	4	1	no	—
189	C₂×C₈	—	4	1	no	—
190	C₂×C₈	C₄²×C₁₃	1	4	yes	—
191	C₄²	—	2	4	no	—
192	C₄²	—	2	4	no	—
193	C₄²	—	2	1	no	—
194	C₄²	—	2	1	no	—
195	C₄²	—	2	1	no	—
196	C₄²	—	2	1	no	—
197	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
198	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
199	C₄²	C₁₃×#41	1	1	yes	characteristic
200	C₄²	C₁₃×#41	1	1	yes	characteristic
201	C₁₃	#8279	1	1	yes	characteristic, direct product factor, Sylow
202	C₂³	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	C₁₃×#108	1	4	yes	—
210	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
211	C₂×C₄	C₁₃×#117	1	1	yes	characteristic
212	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
213	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
214	C₂×C₄	C₄×Q₈×C₁₃	1	1	yes	characteristic
215	C₂×C₄	C₄×Q₈×C₁₃	1	1	yes	characteristic
216	C₂×C₄	C₁₃×#131	1	4	yes	—
217	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
218	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
219	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
220	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
221	C₈	—	2	4	no	—
222	C₈	—	4	2	no	—
223	C₈	—	4	2	no	—
224	C₈	—	4	2	no	—
225	C₈	—	4	2	no	—
226	C₈	—	4	2	no	—
227	C₂²	C₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
228	C₂²	C₁₃×#424	1	2	yes	—
229	C₂²	C₁₃×#428	1	1	yes	characteristic
230	C₂²	C₁₃×#428	1	1	yes	characteristic
231	C₂²	C₂×C₁₃×#108	1	2	yes	—
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	2	4	no	—
235	C₄	—	4	2	no	—
236	C₄	C₁₃×#405	1	2	yes	—
237	C₄	C₁₃×#433	1	2	yes	—
238	C₄	C₁₃×#440	1	1	yes	characteristic
239	C₄	C₁₃×#440	1	1	yes	characteristic
240	C₄	C₁₃×#441	1	1	yes	characteristic
241	C₄	C₁₃×#442	1	1	yes	characteristic
242	C₂	C₁₃×#1573	1	2	yes	—
243	C₂	C₁₃×#1574	1	2	yes	—
244	C₂	C₁₃×#1768	1	1	yes	characteristic
245	C₂	C₁₃×#1776	1	1	yes	characteristic
246	C₂	C₄×C₁₃×#108	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle, prime radical	C₂³×C₁₃	C₂×C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
20. C₁₃×#335	C₄	semidirect
21. C₁₃×#334	C₄	semidirect
47. #8279	C₁₃	direct (N × H)
123. #335	C₄×C₁₃	semidirect
124. #334	C₄×C₁₃	semidirect
201. C₁₃	#8279	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×#1767	2
C₄×C₁₃×C₄⋊C₈	2
C₁₃×#1744	2
C₂×C₁₃×#335	2
C₂×C₁₃×#334	2
C₁₃×#1277	2
#8279	13

Subgroups — C13×#8279 #15694618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#8279 #15694618