Subgroups — C₁₃×#9658 #15695997

Order 3328.

486 conjugacy classes of subgroups.

The subgroup lattice has 258 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	2	no	—
22	C₂×C₁₃×Q₁₆	—	2	2	no	—
23	C₂×C₁₃×Q₁₆	C₈	1	4	yes	complemented
24	C₂²×C₈×C₁₃	—	2	1	no	—
25	C₂²×C₈×C₁₃	—	2	2	no	—
26	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₃	D₄	1	2	yes	—
29	C₄×Q₈×C₁₃	—	2	2	no	—
30	C₄×Q₈×C₁₃	—	2	2	no	—
31	C₄×Q₈×C₁₃	—	2	2	no	—
32	C₄×Q₈×C₁₃	—	2	2	no	—
33	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
34	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
35	C₂×C₄²×C₁₃	—	2	2	no	—
36	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
37	C₁₃×#107	—	2	2	no	—
38	C₁₃×C₄⋊C₈	—	2	2	no	—
39	C₁₃×C₄⋊C₈	—	2	2	no	—
40	C₁₃×#103	—	2	4	no	—
41	C₄×C₈×C₁₃	—	2	1	no	—
42	C₄×C₈×C₁₃	—	2	1	no	—
43	C₄×C₈×C₁₃	—	2	1	no	—
44	C₄×C₈×C₁₃	D₄	1	2	yes	—
45	C₄×C₈×C₁₃	D₄	1	2	yes	—
46	C₄×C₈×C₁₃	D₄	1	2	yes	—
47	#9658	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	2	no	—
53	C₂×Q₈×C₁₃	C₂×C₈	1	4	yes	—
54	C₂²×C₄×C₁₃	—	2	2	no	—
55	C₂²×C₄×C₁₃	—	2	2	no	—
56	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
59	C₁₃×Q₁₆	—	2	8	no	—
60	C₂×C₈×C₁₃	—	2	1	no	—
61	C₂×C₈×C₁₃	—	2	1	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	2	no	—
67	C₂×C₈×C₁₃	—	4	4	no	—
68	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
69	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
70	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
71	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
72	C₁₃×C₄⋊C₄	—	2	2	no	—
73	C₁₃×C₄⋊C₄	—	2	2	no	—
74	C₁₃×C₄⋊C₄	—	4	2	no	—
75	C₁₃×C₄⋊C₄	—	4	2	no	—
76	C₄²×C₁₃	—	4	2	no	—
77	C₄²×C₁₃	—	4	2	no	—
78	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
81	C₄²×C₁₃	#41	1	1	yes	characteristic
82	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic
83	#1984	C₂×C₁₃	1	2	yes	—
84	C₂×#334	C₂×C₁₃	1	1	yes	characteristic
85	C₂×Q₈⋊C₈	C₂×C₁₃	1	2	yes	—
86	C₂×#322	C₂×C₁₃	1	1	yes	characteristic
87	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
88	Q₈×C₁₃	—	2	4	no	—
89	Q₈×C₁₃	—	2	4	no	—
90	Q₈×C₁₃	—	4	2	no	—
91	Q₈×C₁₃	—	4	2	no	—
92	C₂×C₄×C₁₃	—	2	2	no	—
93	C₂×C₄×C₁₃	—	2	4	no	—
94	C₂×C₄×C₁₃	—	4	2	no	—
95	C₂×C₄×C₁₃	—	4	2	no	—
96	C₂×C₄×C₁₃	—	4	2	no	—
97	C₂×C₄×C₁₃	—	4	4	no	—
98	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
100	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
101	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
102	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
103	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
104	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
105	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
106	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
107	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
108	C₂×C₄×C₁₃	#137	1	4	yes	—
109	C₈×C₁₃	—	2	2	no	—
110	C₈×C₁₃	—	4	2	no	—
111	C₈×C₁₃	—	4	2	no	—
112	C₈×C₁₃	—	8	2	no	—
113	C₈×C₁₃	C₂²⋊C₈	1	4	yes	—
114	C₂²×Q₁₆	C₄×C₁₃	1	1	yes	characteristic
115	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
116	C₄×Q₁₆	—	2	2	no	—
117	C₄×Q₁₆	—	2	2	no	—
118	C₂×#107	C₄×C₁₃	1	1	yes	characteristic
119	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
120	C₂×#103	C₄×C₁₃	1	2	yes	—
121	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
122	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
123	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
124	#336	—	2	4	no	—
125	#334	—	2	2	no	—
126	Q₈⋊C₈	—	2	4	no	—
127	#322	—	2	2	no	—
128	C₂²×C₁₃	#390	1	1	yes	characteristic
129	C₂²×C₁₃	C₈×D₄	1	1	yes	characteristic
130	C₂²×C₁₃	#436	1	1	yes	characteristic
131	C₂²×C₁₃	#441	1	2	yes	—
132	C₂²×C₁₃	#444	1	2	yes	—
133	C₄×C₁₃	—	2	1	no	—
134	C₄×C₁₃	—	2	1	no	—
135	C₄×C₁₃	—	4	4	no	—
136	C₄×C₁₃	—	8	2	no	—
137	C₄×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
138	C₄×C₁₃	#408	1	1	yes	characteristic
139	C₄×C₁₃	C₈×D₄	1	1	yes	characteristic
140	C₄×C₁₃	#436	1	1	yes	characteristic
141	C₄×C₁₃	#470	1	2	yes	—
142	C₄×C₁₃	#497	1	2	yes	—
143	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
144	C₂×Q₁₆	—	2	2	no	—
145	C₂×Q₁₆	—	2	2	no	—
146	C₂×Q₁₆	C₈×C₁₃	1	4	yes	complemented
147	C₂²×C₈	—	2	1	no	—
148	C₂²×C₈	—	2	2	no	—
149	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
150	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
151	C₂²×C₈	D₄×C₁₃	1	2	yes	—
152	C₄×Q₈	—	2	2	no	—
153	C₄×Q₈	—	2	2	no	—
154	C₄×Q₈	—	2	2	no	—
155	C₄×Q₈	—	2	2	no	—
156	C₂×C₄⋊C₄	—	2	2	no	—
157	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
158	C₂×C₄²	—	2	2	no	—
159	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
160	#107	—	2	2	no	—
161	C₄⋊C₈	—	2	2	no	—
162	C₄⋊C₈	—	2	2	no	—
163	#103	—	2	4	no	—
164	C₄×C₈	—	2	1	no	—
165	C₄×C₈	—	2	1	no	—
166	C₄×C₈	—	2	1	no	—
167	C₄×C₈	D₄×C₁₃	1	2	yes	—
168	C₄×C₈	D₄×C₁₃	1	2	yes	—
169	C₄×C₈	D₄×C₁₃	1	2	yes	—
170	C₂×C₁₃	#1579	1	2	yes	—
171	C₂×C₁₃	#1593	1	2	yes	—
172	C₂×C₁₃	#1954	1	1	yes	characteristic
173	C₂×C₁₃	#1971	1	1	yes	characteristic
174	C₂×C₁₃	#1975	1	1	yes	characteristic
175	C₂×Q₈	—	2	2	no	—
176	C₂×Q₈	—	2	2	no	—
177	C₂×Q₈	—	2	2	no	—
178	C₂×Q₈	—	2	2	no	—
179	C₂×Q₈	—	2	2	no	—
180	C₂×Q₈	C₂×C₈×C₁₃	1	4	yes	—
181	C₂²×C₄	—	2	2	no	—
182	C₂²×C₄	—	2	2	no	—
183	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
184	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
185	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
186	Q₁₆	—	2	8	no	—
187	C₂×C₈	—	2	1	no	—
188	C₂×C₈	—	2	1	no	—
189	C₂×C₈	—	2	2	no	—
190	C₂×C₈	—	2	2	no	—
191	C₂×C₈	—	2	4	no	—
192	C₂×C₈	—	4	2	no	—
193	C₂×C₈	—	4	2	no	—
194	C₂×C₈	—	4	4	no	—
195	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
196	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
197	C₂×C₈	C₂×C₈×C₁₃	1	2	yes	—
198	C₂×C₈	C₁₃×M₁₆	1	2	yes	—
199	C₄⋊C₄	—	2	2	no	—
200	C₄⋊C₄	—	2	2	no	—
201	C₄⋊C₄	—	4	2	no	—
202	C₄⋊C₄	—	4	2	no	—
203	C₄²	—	4	2	no	—
204	C₄²	—	4	2	no	—
205	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
206	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
207	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
208	C₄²	C₁₃×#41	1	1	yes	characteristic
209	C₁₃	#9658	1	1	yes	characteristic, direct product factor, Sylow
210	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
211	Q₈	—	2	4	no	—
212	Q₈	—	2	4	no	—
213	Q₈	—	4	2	no	—
214	Q₈	—	4	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	4	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	4	4	no	—
221	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
223	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
224	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
225	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
226	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
227	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
228	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
229	C₂×C₄	C₁₃×#131	1	1	yes	characteristic
230	C₂×C₄	C₁₃×#131	1	1	yes	characteristic
231	C₂×C₄	C₁₃×#137	1	4	yes	—
232	C₈	—	2	2	no	—
233	C₈	—	4	2	no	—
234	C₈	—	4	2	no	—
235	C₈	—	8	2	no	—
236	C₈	C₁₃×C₂²⋊C₈	1	4	yes	—
237	C₂²	C₁₃×#390	1	1	yes	characteristic
238	C₂²	C₈×D₄×C₁₃	1	1	yes	characteristic
239	C₂²	C₁₃×#436	1	1	yes	characteristic
240	C₂²	C₁₃×#441	1	2	yes	—
241	C₂²	C₁₃×#444	1	2	yes	—
242	C₄	—	2	1	no	—
243	C₄	—	2	1	no	—
244	C₄	—	4	4	no	—
245	C₄	—	8	2	no	—
246	C₄	C₂×C₁₃×C₂²⋊C₈	1	1	yes	characteristic
247	C₄	C₁₃×#408	1	1	yes	characteristic
248	C₄	C₈×D₄×C₁₃	1	1	yes	characteristic
249	C₄	C₁₃×#436	1	1	yes	characteristic
250	C₄	C₁₃×#470	1	2	yes	—
251	C₄	C₁₃×#497	1	2	yes	—
252	C₂	C₁₃×#1579	1	2	yes	—
253	C₂	C₁₃×#1593	1	2	yes	—
254	C₂	C₁₃×#1954	1	1	yes	characteristic
255	C₂	C₁₃×#1971	1	1	yes	characteristic
256	C₂	C₁₃×#1975	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle, prime radical	C₂³×C₁₃	C₄×D₄
LCS	G ▷ C₂×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
23. C₂×C₁₃×Q₁₆	C₈	semidirect
47. #9658	C₁₃	direct (N × H)
146. C₂×Q₁₆	C₈×C₁₃	semidirect
209. C₁₃	#9658	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
#9658	13

Subgroups — C13×#9658 #15695997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9658 #15695997