Subgroups — C₁₃×#10841 #15697180

Order 3328.

1126 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#384	C₂	1	2	yes	maximal
3	C₂×C₁₃×#340	C₂	1	4	yes	maximal
4	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
5	C₂²×C₁₃×C₄⋊C₄	—	2	4	no	—
6	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
7	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₃	—	2	4	no	—
9	C₂×C₄×C₈×C₁₃	C₄	1	4	yes	complemented
10	C₁₃×#384	—	2	4	no	—
11	C₁₃×#384	C₄	1	8	yes	complemented
12	C₁₃×#340	—	2	8	no	—
13	C₂³×C₄×C₁₃	—	2	4	no	—
14	C₂³×C₄×C₁₃	D₄	1	2	yes	—
15	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
16	C₂²×C₈×C₁₃	—	2	4	no	—
17	C₂²×C₈×C₁₃	—	2	4	no	—
18	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
19	C₂²×C₈×C₁₃	D₄	1	4	yes	—
20	C₂²×C₈×C₁₃	Q₈	1	4	yes	—
21	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
22	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
23	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
24	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
25	C₂×C₁₃×C₄⋊C₄	—	4	8	no	—
26	C₂×C₁₃×C₄⋊C₄	—	4	8	no	—
27	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
28	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
30	C₂×C₄²×C₁₃	D₄	1	4	yes	—
31	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
32	C₄×C₈×C₁₃	—	2	8	no	—
33	#10841	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₃	—	2	8	no	—
36	C₂²×C₄×C₁₃	—	4	4	no	—
37	C₂²×C₄×C₁₃	—	4	4	no	—
38	C₂²×C₄×C₁₃	—	4	8	no	—
39	C₂²×C₄×C₁₃	—	4	8	no	—
40	C₂²×C₄×C₁₃	C₂²⋊C₄	1	8	yes	—
41	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
42	C₂²×C₄×C₁₃	D₈	1	4	yes	—
43	C₂²×C₄×C₁₃	SD₁₆	1	8	yes	—
44	C₂²×C₄×C₁₃	Q₁₆	1	4	yes	—
45	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
47	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
48	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
49	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
51	C₂²×C₄×C₁₃	#41	1	4	yes	—
52	C₂×C₈×C₁₃	—	2	4	no	—
53	C₂×C₈×C₁₃	—	2	4	no	—
54	C₂×C₈×C₁₃	—	2	8	no	—
55	C₂×C₈×C₁₃	—	2	8	no	—
56	C₂×C₈×C₁₃	C₄⋊C₄	1	8	yes	complemented
57	C₁₃×C₄⋊C₄	—	2	16	no	—
58	C₁₃×C₄⋊C₄	—	4	32	no	—
59	C₁₃×C₄⋊C₄	—	4	8	no	—
60	C₄²×C₁₃	C₄²	1	4	yes	—
61	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
62	C₄²×C₁₃	C₄⋊C₄	1	8	yes	—
63	C₂²×C₄×C₈	C₂×C₁₃	1	1	yes	characteristic
64	C₂×#384	C₂×C₁₃	1	2	yes	—
65	C₂×#340	C₂×C₁₃	1	4	yes	—
66	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
67	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
68	C₂³×C₁₃	#124	1	2	yes	—
69	C₂³×C₁₃	#127	1	1	yes	characteristic
70	C₂³×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
71	C₂³×C₁₃	C₂×D₈	1	2	yes	—
72	C₂³×C₁₃	C₂×SD₁₆	1	4	yes	—
73	C₂³×C₁₃	C₂×Q₁₆	1	2	yes	—
74	C₂×C₄×C₁₃	—	4	8	no	—
75	C₂×C₄×C₁₃	—	4	16	no	—
76	C₂×C₄×C₁₃	—	8	8	no	—
77	C₂×C₄×C₁₃	—	8	4	no	—
78	C₂×C₄×C₁₃	—	8	4	no	—
79	C₂×C₄×C₁₃	#95	1	8	yes	—
80	C₂×C₄×C₁₃	#102	1	16	yes	—
81	C₂×C₄×C₁₃	#103	1	16	yes	—
82	C₂×C₄×C₁₃	#106	1	8	yes	—
83	C₂×C₄×C₁₃	#107	1	8	yes	—
84	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
85	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
87	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
88	C₂×C₄×C₁₃	#117	1	2	yes	—
89	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
90	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
91	C₂×C₄×C₁₃	#121	1	4	yes	—
92	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
93	C₂×C₄×C₁₃	#125	1	2	yes	—
94	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
95	C₈×C₁₃	—	2	8	no	—
96	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
97	C₂²×C₄⋊C₄	—	2	4	no	—
98	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
99	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
100	C₂×C₄×C₈	—	2	4	no	—
101	C₂×C₄×C₈	C₄×C₁₃	1	4	yes	complemented
102	#384	—	2	4	no	—
103	#384	C₄×C₁₃	1	8	yes	complemented
104	#340	—	2	8	no	—
105	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
106	C₂²×C₁₃	#382	1	1	yes	characteristic
107	C₂²×C₁₃	#384	1	1	yes	characteristic
108	C₂²×C₁₃	#390	1	2	yes	—
109	C₂²×C₁₃	#391	1	2	yes	—
110	C₂²×C₁₃	C₂×#102	1	4	yes	—
111	C₂²×C₁₃	C₂×#103	1	4	yes	—
112	C₂²×C₁₃	C₂×#106	1	2	yes	—
113	C₂²×C₁₃	C₂×#107	1	2	yes	—
114	C₂²×C₁₃	#486	1	4	yes	—
115	C₂²×C₁₃	#487	1	4	yes	—
116	C₂²×C₁₃	#492	1	2	yes	—
117	C₂²×C₁₃	#493	1	1	yes	characteristic
118	C₂²×C₁₃	#494	1	1	yes	characteristic
119	C₂²×C₁₃	#498	1	2	yes	—
120	C₂²×C₁₃	#500	1	2	yes	—
121	C₄×C₁₃	—	8	8	no	—
122	C₄×C₁₃	#340	1	16	yes	complemented
123	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
124	C₄×C₁₃	#380	1	2	yes	—
125	C₄×C₁₃	#389	1	4	yes	—
126	C₂³×C₄	—	2	4	no	—
127	C₂³×C₄	D₄×C₁₃	1	2	yes	—
128	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
129	C₂²×C₈	—	2	4	no	—
130	C₂²×C₈	—	2	4	no	—
131	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
132	C₂²×C₈	D₄×C₁₃	1	4	yes	—
133	C₂²×C₈	Q₈×C₁₃	1	4	yes	—
134	C₂×C₄⋊C₄	—	2	8	no	—
135	C₂×C₄⋊C₄	—	2	8	no	—
136	C₂×C₄⋊C₄	—	2	16	no	—
137	C₂×C₄⋊C₄	—	2	4	no	—
138	C₂×C₄⋊C₄	—	4	8	no	—
139	C₂×C₄⋊C₄	—	4	8	no	—
140	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
141	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
142	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
143	C₂×C₄²	D₄×C₁₃	1	4	yes	—
144	C₂×C₄²	Q₈×C₁₃	1	2	yes	—
145	C₄×C₈	—	2	8	no	—
146	C₂×C₁₃	C₄⋊#95	1	1	yes	characteristic
147	C₂×C₁₃	C₂×#340	1	2	yes	—
148	C₂×C₁₃	#1834	1	2	yes	—
149	C₂×C₁₃	#1844	1	1	yes	characteristic
150	C₂×C₁₃	#1845	1	1	yes	characteristic
151	C₂×C₁₃	#1956	1	2	yes	—
152	C₂×C₁₃	#1957	1	2	yes	—
153	C₂×C₁₃	#1990	1	4	yes	—
154	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
155	C₂²×C₄	—	2	8	no	—
156	C₂²×C₄	—	4	4	no	—
157	C₂²×C₄	—	4	4	no	—
158	C₂²×C₄	—	4	8	no	—
159	C₂²×C₄	—	4	8	no	—
160	C₂²×C₄	C₁₃×C₂²⋊C₄	1	8	yes	—
161	C₂²×C₄	C₁₃×C₄⋊C₄	1	4	yes	—
162	C₂²×C₄	C₁₃×D₈	1	4	yes	—
163	C₂²×C₄	C₁₃×SD₁₆	1	8	yes	—
164	C₂²×C₄	C₁₃×Q₁₆	1	4	yes	—
165	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
166	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
167	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
168	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
169	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
170	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
171	C₂²×C₄	C₁₃×#41	1	4	yes	—
172	C₂×C₈	—	2	4	no	—
173	C₂×C₈	—	2	4	no	—
174	C₂×C₈	—	2	8	no	—
175	C₂×C₈	—	2	8	no	—
176	C₂×C₈	C₁₃×C₄⋊C₄	1	8	yes	complemented
177	C₄⋊C₄	—	2	16	no	—
178	C₄⋊C₄	—	4	32	no	—
179	C₄⋊C₄	—	4	8	no	—
180	C₄²	C₄²×C₁₃	1	4	yes	—
181	C₄²	C₁₃×C₂²⋊C₄	1	4	yes	—
182	C₄²	C₁₃×C₄⋊C₄	1	8	yes	—
183	C₁₃	#10841	1	1	yes	characteristic, direct product factor, Sylow
184	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
185	C₂³	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
186	C₂³	C₁₃×#124	1	2	yes	—
187	C₂³	C₁₃×#127	1	1	yes	characteristic
188	C₂³	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
189	C₂³	C₂×C₁₃×D₈	1	2	yes	—
190	C₂³	C₂×C₁₃×SD₁₆	1	4	yes	—
191	C₂³	C₂×C₁₃×Q₁₆	1	2	yes	—
192	C₂×C₄	—	4	8	no	—
193	C₂×C₄	—	4	16	no	—
194	C₂×C₄	—	8	8	no	—
195	C₂×C₄	—	8	4	no	—
196	C₂×C₄	—	8	4	no	—
197	C₂×C₄	C₁₃×#95	1	8	yes	—
198	C₂×C₄	C₁₃×#102	1	16	yes	—
199	C₂×C₄	C₁₃×#103	1	16	yes	—
200	C₂×C₄	C₁₃×#106	1	8	yes	—
201	C₂×C₄	C₁₃×#107	1	8	yes	—
202	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
203	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
205	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
206	C₂×C₄	C₁₃×#117	1	2	yes	—
207	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
208	C₂×C₄	C₄×Q₈×C₁₃	1	4	yes	—
209	C₂×C₄	C₁₃×#121	1	4	yes	—
210	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
211	C₂×C₄	C₁₃×#125	1	2	yes	—
212	C₂×C₄	C₁₃×C₄⋊Q₈	1	2	yes	—
213	C₈	—	2	8	no	—
214	C₂²	C₂×C₁₃×#95	1	1	yes	characteristic
215	C₂²	C₁₃×#382	1	1	yes	characteristic
216	C₂²	C₁₃×#384	1	1	yes	characteristic
217	C₂²	C₁₃×#390	1	2	yes	—
218	C₂²	C₁₃×#391	1	2	yes	—
219	C₂²	C₂×C₁₃×#102	1	4	yes	—
220	C₂²	C₂×C₁₃×#103	1	4	yes	—
221	C₂²	C₂×C₁₃×#106	1	2	yes	—
222	C₂²	C₂×C₁₃×#107	1	2	yes	—
223	C₂²	C₁₃×#486	1	4	yes	—
224	C₂²	C₁₃×#487	1	4	yes	—
225	C₂²	C₁₃×#492	1	2	yes	—
226	C₂²	C₁₃×#493	1	1	yes	characteristic
227	C₂²	C₁₃×#494	1	1	yes	characteristic
228	C₂²	C₁₃×#498	1	2	yes	—
229	C₂²	C₁₃×#500	1	2	yes	—
230	C₄	—	8	8	no	—
231	C₄	C₁₃×#340	1	16	yes	complemented
232	C₄	C₄×C₁₃×C₄⋊C₄	1	2	yes	—
233	C₄	C₁₃×#380	1	2	yes	—
234	C₄	C₁₃×#389	1	4	yes	—
235	C₂	C₁₃×C₄⋊#95	1	1	yes	characteristic
236	C₂	C₂×C₁₃×#340	1	2	yes	—
237	C₂	C₁₃×#1834	1	2	yes	—
238	C₂	C₁₃×#1844	1	1	yes	characteristic
239	C₂	C₁₃×#1845	1	1	yes	characteristic
240	C₂	C₁₃×#1956	1	2	yes	—
241	C₂	C₁₃×#1957	1	2	yes	—
242	C₂	C₁₃×#1990	1	4	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
9. C₂×C₄×C₈×C₁₃	C₄	semidirect
11. C₁₃×#384	C₄	semidirect
33. #10841	C₁₃	direct (N × H)
56. C₂×C₈×C₁₃	C₄⋊C₄	semidirect
101. C₂×C₄×C₈	C₄×C₁₃	semidirect
103. #384	C₄×C₁₃	semidirect
122. C₄×C₁₃	#340	semidirect
176. C₂×C₈	C₁₃×C₄⋊C₄	semidirect
183. C₁₃	#10841	direct (N × H)
231. C₄	C₁₃×#340	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₄×C₈×C₁₃	2
C₂×C₁₃×#384	2
C₂×C₁₃×#340	2
#10841	13

Subgroups — C13×#10841 #15697180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10841 #15697180