Subgroups — C₁₃×#9664 #15696003

Order 3328.

482 conjugacy classes of subgroups.

The subgroup lattice has 242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1984	C₂	1	2	yes	maximal
3	C₂×C₁₃×#334	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×Q₈⋊C₈	C₂	1	2	yes	maximal
5	C₂×C₁₃×#322	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×Q₁₆	C₄	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
8	C₄×C₁₃×Q₁₆	—	2	2	no	—
9	C₄×C₁₃×Q₁₆	—	2	2	no	—
10	C₂×C₁₃×#107	C₄	1	1	yes	characteristic
11	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
12	C₂×C₁₃×#103	C₄	1	2	yes	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#336	—	2	4	no	—
17	C₁₃×#334	—	2	2	no	—
18	C₁₃×Q₈⋊C₈	—	2	4	no	—
19	C₁₃×#322	—	2	2	no	—
20	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
21	C₂×C₁₃×Q₁₆	—	2	4	no	—
22	C₂×C₁₃×Q₁₆	—	2	2	no	—
23	C₂²×C₈×C₁₃	—	2	1	no	—
24	C₂²×C₈×C₁₃	—	2	2	no	—
25	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	D₄	1	2	yes	—
28	C₄×Q₈×C₁₃	—	2	2	no	—
29	C₄×Q₈×C₁₃	—	2	2	no	—
30	C₄×Q₈×C₁₃	—	2	2	no	—
31	C₄×Q₈×C₁₃	—	2	2	no	—
32	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
33	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
34	C₂×C₄²×C₁₃	—	2	2	no	—
35	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
36	C₁₃×#107	—	2	2	no	—
37	C₁₃×C₄⋊C₈	—	2	2	no	—
38	C₁₃×C₄⋊C₈	—	2	2	no	—
39	C₁₃×#103	—	2	4	no	—
40	C₄×C₈×C₁₃	—	2	1	no	—
41	C₄×C₈×C₁₃	—	2	1	no	—
42	C₄×C₈×C₁₃	—	2	1	no	—
43	C₄×C₈×C₁₃	D₄	1	2	yes	—
44	C₄×C₈×C₁₃	D₄	1	2	yes	—
45	C₄×C₈×C₁₃	D₄	1	2	yes	—
46	#9664	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂×Q₈×C₁₃	—	2	2	no	—
48	C₂×Q₈×C₁₃	—	2	2	no	—
49	C₂×Q₈×C₁₃	—	2	2	no	—
50	C₂×Q₈×C₁₃	—	2	2	no	—
51	C₂×Q₈×C₁₃	—	2	2	no	—
52	C₂×Q₈×C₁₃	M₁₆	1	4	yes	—
53	C₂²×C₄×C₁₃	—	2	2	no	—
54	C₂²×C₄×C₁₃	—	2	2	no	—
55	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
58	C₁₃×Q₁₆	—	2	8	no	—
59	C₂×C₈×C₁₃	—	2	4	no	—
60	C₂×C₈×C₁₃	—	2	2	no	—
61	C₂×C₈×C₁₃	—	2	2	no	—
62	C₂×C₈×C₁₃	—	2	2	no	—
63	C₂×C₈×C₁₃	—	2	2	no	—
64	C₂×C₈×C₁₃	—	2	4	no	—
65	C₂×C₈×C₁₃	—	4	2	no	—
66	C₂×C₈×C₁₃	—	4	4	no	—
67	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
68	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
69	C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₁₃×C₄⋊C₄	—	2	2	no	—
71	C₁₃×C₄⋊C₄	—	4	2	no	—
72	C₁₃×C₄⋊C₄	—	4	2	no	—
73	C₄²×C₁₃	—	4	2	no	—
74	C₄²×C₁₃	—	4	2	no	—
75	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₁₃	#41	1	1	yes	characteristic
79	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic
80	#1984	C₂×C₁₃	1	2	yes	—
81	C₂×#334	C₂×C₁₃	1	1	yes	characteristic
82	C₂×Q₈⋊C₈	C₂×C₁₃	1	2	yes	—
83	C₂×#322	C₂×C₁₃	1	1	yes	characteristic
84	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
85	Q₈×C₁₃	—	2	4	no	—
86	Q₈×C₁₃	—	2	4	no	—
87	Q₈×C₁₃	—	4	2	no	—
88	Q₈×C₁₃	—	4	2	no	—
89	C₂×C₄×C₁₃	—	2	2	no	—
90	C₂×C₄×C₁₃	—	2	4	no	—
91	C₂×C₄×C₁₃	—	4	2	no	—
92	C₂×C₄×C₁₃	—	4	2	no	—
93	C₂×C₄×C₁₃	—	4	2	no	—
94	C₂×C₄×C₁₃	—	4	4	no	—
95	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
97	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
98	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
99	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
100	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
101	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
102	C₂×C₄×C₁₃	#131	1	2	yes	—
103	C₂×C₄×C₁₃	#137	1	4	yes	—
104	C₈×C₁₃	—	2	4	no	—
105	C₈×C₁₃	—	2	2	no	—
106	C₈×C₁₃	—	2	2	no	—
107	C₈×C₁₃	—	4	2	no	—
108	C₈×C₁₃	—	8	2	no	—
109	C₂²×Q₁₆	C₄×C₁₃	1	1	yes	characteristic
110	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
111	C₄×Q₁₆	—	2	2	no	—
112	C₄×Q₁₆	—	2	2	no	—
113	C₂×#107	C₄×C₁₃	1	1	yes	characteristic
114	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
115	C₂×#103	C₄×C₁₃	1	2	yes	—
116	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
117	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
118	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
119	#336	—	2	4	no	—
120	#334	—	2	2	no	—
121	Q₈⋊C₈	—	2	4	no	—
122	#322	—	2	2	no	—
123	C₂²×C₁₃	#390	1	1	yes	characteristic
124	C₂²×C₁₃	#435	1	2	yes	—
125	C₂²×C₁₃	#441	1	2	yes	—
126	C₂²×C₁₃	#443	1	2	yes	—
127	C₄×C₁₃	—	2	1	no	—
128	C₄×C₁₃	—	2	1	no	—
129	C₄×C₁₃	—	4	4	no	—
130	C₄×C₁₃	—	8	2	no	—
131	C₄×C₁₃	#407	1	1	yes	characteristic
132	C₄×C₁₃	#408	1	1	yes	characteristic
133	C₄×C₁₃	#435	1	2	yes	—
134	C₄×C₁₃	#470	1	2	yes	—
135	C₄×C₁₃	#497	1	2	yes	—
136	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
137	C₂×Q₁₆	—	2	4	no	—
138	C₂×Q₁₆	—	2	2	no	—
139	C₂²×C₈	—	2	1	no	—
140	C₂²×C₈	—	2	2	no	—
141	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
142	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
143	C₂²×C₈	D₄×C₁₃	1	2	yes	—
144	C₄×Q₈	—	2	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	C₄×Q₈	—	2	2	no	—
148	C₂×C₄⋊C₄	—	2	2	no	—
149	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
150	C₂×C₄²	—	2	2	no	—
151	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
152	#107	—	2	2	no	—
153	C₄⋊C₈	—	2	2	no	—
154	C₄⋊C₈	—	2	2	no	—
155	#103	—	2	4	no	—
156	C₄×C₈	—	2	1	no	—
157	C₄×C₈	—	2	1	no	—
158	C₄×C₈	—	2	1	no	—
159	C₄×C₈	D₄×C₁₃	1	2	yes	—
160	C₄×C₈	D₄×C₁₃	1	2	yes	—
161	C₄×C₈	D₄×C₁₃	1	2	yes	—
162	C₂×C₁₃	#1587	1	4	yes	—
163	C₂×C₁₃	#1955	1	1	yes	characteristic
164	C₂×C₁₃	#1971	1	1	yes	characteristic
165	C₂×C₁₃	#1974	1	1	yes	characteristic
166	C₂×Q₈	—	2	2	no	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	2	no	—
169	C₂×Q₈	—	2	2	no	—
170	C₂×Q₈	—	2	2	no	—
171	C₂×Q₈	C₁₃×M₁₆	1	4	yes	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
175	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
176	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
177	Q₁₆	—	2	8	no	—
178	C₂×C₈	—	2	4	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	2	4	no	—
184	C₂×C₈	—	4	2	no	—
185	C₂×C₈	—	4	4	no	—
186	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
187	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
188	C₄⋊C₄	—	2	2	no	—
189	C₄⋊C₄	—	2	2	no	—
190	C₄⋊C₄	—	4	2	no	—
191	C₄⋊C₄	—	4	2	no	—
192	C₄²	—	4	2	no	—
193	C₄²	—	4	2	no	—
194	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
195	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
196	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
197	C₄²	C₁₃×#41	1	1	yes	characteristic
198	C₁₃	#9664	1	1	yes	characteristic, direct product factor, Sylow
199	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
200	Q₈	—	2	4	no	—
201	Q₈	—	2	4	no	—
202	Q₈	—	4	2	no	—
203	Q₈	—	4	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	4	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	4	no	—
210	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
212	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
213	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
214	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
215	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
216	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
217	C₂×C₄	C₁₃×#131	1	2	yes	—
218	C₂×C₄	C₁₃×#137	1	4	yes	—
219	C₈	—	2	4	no	—
220	C₈	—	2	2	no	—
221	C₈	—	2	2	no	—
222	C₈	—	4	2	no	—
223	C₈	—	8	2	no	—
224	C₂²	C₁₃×#390	1	1	yes	characteristic
225	C₂²	C₁₃×#435	1	2	yes	—
226	C₂²	C₁₃×#441	1	2	yes	—
227	C₂²	C₁₃×#443	1	2	yes	—
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	4	4	no	—
231	C₄	—	8	2	no	—
232	C₄	C₁₃×#407	1	1	yes	characteristic
233	C₄	C₁₃×#408	1	1	yes	characteristic
234	C₄	C₁₃×#435	1	2	yes	—
235	C₄	C₁₃×#470	1	2	yes	—
236	C₄	C₁₃×#497	1	2	yes	—
237	C₂	C₁₃×#1587	1	4	yes	—
238	C₂	C₁₃×#1955	1	1	yes	characteristic
239	C₂	C₁₃×#1971	1	1	yes	characteristic
240	C₂	C₁₃×#1974	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle, prime radical	C₂³×C₁₃	C₄×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
46. #9664	C₁₃	direct (N × H)
198. C₁₃	#9664	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×C₄×C₁₃×Q₁₆	2
C₁₃×#1984	2
C₂×C₁₃×#334	2
C₂×C₁₃×Q₈⋊C₈	2
C₂×C₁₃×#322	2
#9664	13

Subgroups — C13×#9664 #15696003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9664 #15696003