Subgroups — C₁₃×#11662 #15698001

Order 3328.

358 conjugacy classes of subgroups.

The subgroup lattice has 234 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×#2162	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1568	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1332	C₂	1	4	yes	maximal, complemented
5	C₂²×C₁₃×Q₁₆	C₄	1	1	yes	characteristic
6	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
7	C₄×C₁₃×Q₁₆	—	2	1	no	—
8	C₄×C₁₃×Q₁₆	—	2	1	no	—
9	C₄×C₁₃×Q₁₆	C₄	1	2	yes	—
10	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
11	C₁₃×#432	—	2	1	no	—
12	C₂×C₁₃×#107	C₄	1	1	yes	characteristic
13	C₂×C₁₃×#103	—	2	1	no	—
14	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×C₄⋊C₁₆	—	2	1	no	—
16	C₁₃×C₂²⋊C₁₆	—	2	1	no	—
17	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
18	C₁₃×#335	C₂²	1	2	yes	—
19	C₁₃×#334	—	2	1	no	—
20	C₂²×Q₈×C₁₃	—	2	1	no	—
21	C₂×C₁₃×Q₁₆	—	2	4	no	—
22	C₂×C₁₃×Q₁₆	—	2	1	no	—
23	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
26	C₄×Q₈×C₁₃	—	2	2	no	—
27	C₄×Q₈×C₁₃	—	2	2	no	—
28	C₄×Q₈×C₁₃	—	4	1	no	—
29	C₄×Q₈×C₁₃	—	4	1	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
31	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
32	C₂×C₄²×C₁₃	—	4	1	no	—
33	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
34	C₂×C₁₃×C₁₆	—	2	2	no	—
35	C₁₃×#107	—	2	1	no	—
36	C₁₃×#107	C₂×C₄	1	2	yes	—
37	C₁₃×C₄⋊C₈	—	2	2	no	—
38	C₁₃×#103	—	2	2	no	—
39	C₁₃×#103	—	2	2	no	—
40	C₁₃×C₂²⋊C₈	—	4	1	no	—
41	C₁₃×#97	—	4	1	no	—
42	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
44	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
45	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	#11662	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂×Q₈×C₁₃	—	2	4	no	—
48	C₂×Q₈×C₁₃	—	2	2	no	—
49	C₂×Q₈×C₁₃	—	4	2	no	—
50	C₂×Q₈×C₁₃	—	4	1	no	—
51	C₂²×C₄×C₁₃	—	4	1	no	—
52	C₂²×C₄×C₁₃	—	4	1	no	—
53	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	SD₁₆	1	1	yes	characteristic
56	C₁₃×Q₁₆	—	2	4	no	—
57	C₁₃×Q₁₆	—	2	2	no	—
58	C₁₃×Q₁₆	M₁₆	1	4	yes	—
59	C₂×C₈×C₁₃	—	2	2	no	—
60	C₂×C₈×C₁₃	—	4	1	no	—
61	C₂×C₈×C₁₃	—	4	2	no	—
62	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
66	C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₁₃×C₄⋊C₄	—	4	1	no	—
68	C₁₃×C₄⋊C₄	—	4	2	no	—
69	C₁₃×C₄⋊C₄	—	4	2	no	—
70	C₄²×C₁₃	—	4	2	no	—
71	C₄²×C₁₃	—	4	2	no	—
72	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₄²×C₁₃	D₈	1	1	yes	characteristic
74	C₄²×C₁₃	SD₁₆	1	1	yes	characteristic
75	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
76	C₁₃×C₁₆	—	4	2	no	—
77	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic
78	#2162	C₂×C₁₃	1	1	yes	characteristic
79	#1568	C₂×C₁₃	1	1	yes	characteristic
80	#1332	C₂×C₁₃	1	4	yes	complemented
81	C₂³×C₁₃	#102	1	1	yes	characteristic
82	Q₈×C₁₃	—	2	4	no	—
83	Q₈×C₁₃	—	4	4	no	—
84	Q₈×C₁₃	—	4	2	no	—
85	C₂×C₄×C₁₃	—	2	2	no	—
86	C₂×C₄×C₁₃	—	2	1	no	—
87	C₂×C₄×C₁₃	—	2	1	no	—
88	C₂×C₄×C₁₃	—	2	2	no	—
89	C₂×C₄×C₁₃	—	4	4	no	—
90	C₂×C₄×C₁₃	—	4	2	no	—
91	C₂×C₄×C₁₃	—	4	2	no	—
92	C₂×C₄×C₁₃	—	8	2	no	—
93	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
94	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
95	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
96	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
98	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
99	C₈×C₁₃	—	2	1	no	—
100	C₈×C₁₃	—	2	1	no	—
101	C₈×C₁₃	—	2	1	no	—
102	C₈×C₁₃	—	8	2	no	—
103	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
104	C₂²×Q₁₆	C₄×C₁₃	1	1	yes	characteristic
105	C₂×C₄×Q₈	—	2	1	no	—
106	C₄×Q₁₆	—	2	1	no	—
107	C₄×Q₁₆	—	2	1	no	—
108	C₄×Q₁₆	C₄×C₁₃	1	2	yes	—
109	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
110	#432	—	2	1	no	—
111	C₂×#107	C₄×C₁₃	1	1	yes	characteristic
112	C₂×#103	—	2	1	no	—
113	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
114	C₄⋊C₁₆	—	2	1	no	—
115	C₂²⋊C₁₆	—	2	1	no	—
116	C₄×C₁₆	C₂²×C₁₃	1	2	yes	—
117	#335	C₂²×C₁₃	1	2	yes	—
118	#334	—	2	1	no	—
119	C₂²×C₁₃	—	2	1	no	—
120	C₂²×C₁₃	—	2	1	no	—
121	C₂²×C₁₃	#359	1	2	yes	—
122	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
123	C₄×C₁₃	—	2	1	no	—
124	C₄×C₁₃	—	2	1	no	—
125	C₄×C₁₃	—	2	1	no	—
126	C₄×C₁₃	—	2	1	no	—
127	C₄×C₁₃	—	4	4	no	—
128	C₄×C₁₃	—	8	2	no	—
129	C₄×C₁₃	#407	1	1	yes	characteristic
130	C₄×C₁₃	#421	1	1	yes	characteristic
131	C₄×C₁₃	#510	1	2	yes	—
132	C₂²×Q₈	—	2	1	no	—
133	C₂×Q₁₆	—	2	4	no	—
134	C₂×Q₁₆	—	2	1	no	—
135	C₂×Q₁₆	C₂×C₄×C₁₃	1	2	yes	—
136	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
137	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
138	C₄×Q₈	—	2	2	no	—
139	C₄×Q₈	—	2	2	no	—
140	C₄×Q₈	—	4	1	no	—
141	C₄×Q₈	—	4	1	no	—
142	C₂×C₄⋊C₄	—	2	1	no	—
143	C₂×C₄⋊C₄	—	4	1	no	—
144	C₂×C₄²	—	4	1	no	—
145	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
146	C₂×C₁₆	—	2	2	no	—
147	#107	—	2	1	no	—
148	#107	C₂×C₄×C₁₃	1	2	yes	—
149	C₄⋊C₈	—	2	2	no	—
150	#103	—	2	2	no	—
151	#103	—	2	2	no	—
152	C₂²⋊C₈	—	4	1	no	—
153	#97	—	4	1	no	—
154	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
155	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
156	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
157	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
158	C₂×C₁₃	—	2	2	no	—
159	C₂×C₁₃	#1486	1	1	yes	characteristic
160	C₂×C₁₃	#2141	1	1	yes	characteristic
161	C₂×C₁₃	C₂×#359	1	1	yes	characteristic
162	C₂×Q₈	—	2	4	no	—
163	C₂×Q₈	—	2	2	no	—
164	C₂×Q₈	—	4	2	no	—
165	C₂×Q₈	—	4	1	no	—
166	C₂²×C₄	—	4	1	no	—
167	C₂²×C₄	—	4	1	no	—
168	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
169	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
170	C₂²×C₄	C₁₃×SD₁₆	1	1	yes	characteristic
171	Q₁₆	—	2	4	no	—
172	Q₁₆	—	2	2	no	—
173	Q₁₆	C₁₃×M₁₆	1	4	yes	—
174	C₂×C₈	—	2	2	no	—
175	C₂×C₈	—	4	1	no	—
176	C₂×C₈	—	4	2	no	—
177	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
180	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
181	C₄⋊C₄	—	2	2	no	—
182	C₄⋊C₄	—	4	1	no	—
183	C₄⋊C₄	—	4	2	no	—
184	C₄⋊C₄	—	4	2	no	—
185	C₄²	—	4	2	no	—
186	C₄²	—	4	2	no	—
187	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
188	C₄²	C₁₃×D₈	1	1	yes	characteristic
189	C₄²	C₁₃×SD₁₆	1	1	yes	characteristic
190	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
191	C₁₆	—	4	2	no	—
192	C₁₃	#11662	1	1	yes	characteristic, direct product factor, Sylow
193	C₂³	C₁₃×#102	1	1	yes	characteristic
194	Q₈	—	2	4	no	—
195	Q₈	—	4	4	no	—
196	Q₈	—	4	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	4	4	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	8	2	no	—
205	C₂×C₄	C₁₃×#102	1	1	yes	characteristic
206	C₂×C₄	C₁₃×#102	1	1	yes	characteristic
207	C₂×C₄	C₁₃×#102	1	1	yes	characteristic
208	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
210	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
211	C₈	—	2	1	no	—
212	C₈	—	2	1	no	—
213	C₈	—	2	1	no	—
214	C₈	—	8	2	no	—
215	C₈	C₂×C₁₃×M₁₆	1	2	yes	—
216	C₂²	—	2	1	no	—
217	C₂²	—	2	1	no	—
218	C₂²	C₁₃×#359	1	2	yes	—
219	C₂²	C₂×C₁₃×#102	1	1	yes	characteristic
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	4	4	no	—
225	C₄	—	8	2	no	—
226	C₄	C₁₃×#407	1	1	yes	characteristic
227	C₄	C₁₃×#421	1	1	yes	characteristic
228	C₄	C₁₃×#510	1	2	yes	—
229	C₂	—	2	2	no	—
230	C₂	C₁₃×#1486	1	1	yes	characteristic
231	C₂	C₁₃×#2141	1	1	yes	characteristic
232	C₂	C₂×C₁₃×#359	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₄×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×#102
prime radical	C₂³×C₁₃	#102
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#1332	C₂	semidirect
46. #11662	C₁₃	direct (N × H)
80. #1332	C₂×C₁₃	semidirect
192. C₁₃	#11662	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×#2162	2
C₁₃×#1568	2
C₁₃×#1332	2
#11662	13

Subgroups — C13×#11662 #15698001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#11662 #15698001