Subgroups — C₁₃×#9648 #15695987

Order 3328.

726 conjugacy classes of subgroups.

The subgroup lattice has 246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×#127	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1831	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×D₄⋊C₈	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#127	C₄	1	1	yes	characteristic
6	C₂×C₄×D₄×C₁₃	—	2	2	no	—
7	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
8	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
9	C₂×C₁₃×#97	—	2	2	no	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
11	C₁₃×#390	—	2	2	no	—
12	C₁₃×#390	C₄	1	2	yes	—
13	C₁₃×#384	C₄	1	1	yes	characteristic
14	C₄³×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#336	—	2	2	no	—
16	C₁₃×D₄⋊C₈	—	2	8	no	—
17	C₂²×D₄×C₁₃	—	2	2	no	—
18	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
19	C₂³×C₄×C₁₃	—	2	2	no	—
20	C₂²×C₈×C₁₃	—	2	2	no	—
21	C₂²×C₈×C₁₃	—	2	2	no	—
22	C₁₃×#127	—	2	4	no	—
23	C₄×D₄×C₁₃	—	2	4	no	—
24	C₄×D₄×C₁₃	—	2	4	no	—
25	C₄×D₄×C₁₃	—	4	8	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
27	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
28	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
29	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
30	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₃	D₄	1	2	yes	—
33	C₂×C₄²×C₁₃	D₄	1	2	yes	—
34	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
35	C₁₃×C₄⋊C₈	—	2	4	no	—
36	C₁₃×#97	—	2	8	no	—
37	C₄×C₈×C₁₃	—	2	2	no	—
38	C₄×C₈×C₁₃	D₄	1	4	yes	complemented
39	#9648	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂⁴×C₁₃	—	2	2	no	—
41	C₂×D₄×C₁₃	—	2	8	no	—
42	C₂×D₄×C₁₃	—	2	4	no	—
43	C₂×D₄×C₁₃	—	2	2	no	—
44	C₂×D₄×C₁₃	—	2	4	no	—
45	C₂×D₄×C₁₃	—	4	4	no	—
46	C₂×D₄×C₁₃	—	4	4	no	—
47	C₂×D₄×C₁₃	M₁₆	1	4	yes	—
48	C₂²×C₄×C₁₃	—	2	2	no	—
49	C₂²×C₄×C₁₃	—	4	2	no	—
50	C₂²×C₄×C₁₃	—	4	2	no	—
51	C₂²×C₄×C₁₃	—	4	8	no	—
52	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
53	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
54	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
57	C₂×C₈×C₁₃	—	2	8	no	—
58	C₂×C₈×C₁₃	—	2	4	no	—
59	C₂×C₈×C₁₃	—	4	2	no	—
60	C₂×C₈×C₁₃	—	4	4	no	—
61	C₁₃×C₄⋊C₄	—	2	4	no	—
62	C₁₃×C₄⋊C₄	—	4	4	no	—
63	C₁₃×C₂²⋊C₄	—	4	8	no	—
64	C₁₃×C₂²⋊C₄	—	4	4	no	—
65	C₄²×C₁₃	—	2	4	no	—
66	C₄²×C₁₃	—	2	2	no	—
67	C₄²×C₁₃	—	2	2	no	—
68	C₄²×C₁₃	—	2	4	no	—
69	C₄²×C₁₃	C₂×D₄	1	2	yes	—
70	C₄²×C₁₃	#41	1	2	yes	—
71	C₄×#127	C₂×C₁₃	1	1	yes	characteristic
72	#1831	C₂×C₁₃	1	1	yes	characteristic, complemented
73	C₄×#97	C₂×C₁₃	1	1	yes	characteristic, complemented
74	C₂×D₄⋊C₈	C₂×C₁₃	1	4	yes	complemented
75	C₂³×C₁₃	—	2	4	no	—
76	C₂³×C₁₃	—	4	2	no	—
77	C₂³×C₁₃	—	4	2	no	—
78	C₂³×C₁₃	—	4	4	no	—
79	C₂³×C₁₃	—	4	4	no	—
80	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	D₄×C₁₃	—	2	8	no	—
82	D₄×C₁₃	—	4	16	no	—
83	D₄×C₁₃	—	4	4	no	—
84	C₂×C₄×C₁₃	—	2	2	no	—
85	C₂×C₄×C₁₃	—	2	2	no	—
86	C₂×C₄×C₁₃	—	2	2	no	—
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	—	4	2	no	—
91	C₂×C₄×C₁₃	—	4	4	no	—
92	C₂×C₄×C₁₃	—	8	4	no	—
93	C₂×C₄×C₁₃	—	8	4	no	—
94	C₂×C₄×C₁₃	#104	1	4	yes	—
95	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
96	C₂×C₄×C₁₃	#121	1	2	yes	—
97	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
98	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
99	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
100	C₂×C₄×C₁₃	#131	1	2	yes	—
101	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
102	C₈×C₁₃	—	2	8	no	—
103	C₈×C₁₃	—	8	2	no	—
104	C₂×#127	C₄×C₁₃	1	1	yes	characteristic
105	C₂×C₄×D₄	—	2	2	no	—
106	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
107	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
108	C₂×#97	—	2	2	no	—
109	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
110	#390	—	2	2	no	—
111	#390	C₄×C₁₃	1	2	yes	—
112	#384	C₄×C₁₃	1	1	yes	characteristic
113	C₄³	C₂²×C₁₃	1	1	yes	characteristic
114	#336	—	2	2	no	—
115	D₄⋊C₈	—	2	8	no	—
116	C₂²×C₁₃	—	4	4	no	—
117	C₂²×C₁₃	—	4	8	no	—
118	C₂²×C₁₃	—	8	2	no	—
119	C₂²×C₁₃	—	8	2	no	—
120	C₂²×C₁₃	—	8	4	no	—
121	C₂²×C₁₃	#390	1	1	yes	characteristic
122	C₂²×C₁₃	#407	1	1	yes	characteristic
123	C₂²×C₁₃	#408	1	1	yes	characteristic
124	C₂²×C₁₃	#418	1	2	yes	—
125	C₂²×C₁₃	C₂×#104	1	2	yes	—
126	C₄×C₁₃	—	2	2	no	—
127	C₄×C₁₃	—	2	4	no	—
128	C₄×C₁₃	—	4	2	no	—
129	C₄×C₁₃	—	8	2	no	—
130	C₄×C₁₃	#435	1	4	yes	—
131	C₄×C₁₃	#490	1	2	yes	—
132	C₄×C₁₃	#496	1	2	yes	—
133	C₂²×D₄	—	2	2	no	—
134	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
135	C₂³×C₄	—	2	2	no	—
136	C₂²×C₈	—	2	2	no	—
137	C₂²×C₈	—	2	2	no	—
138	#127	—	2	4	no	—
139	C₄×D₄	—	2	4	no	—
140	C₄×D₄	—	2	4	no	—
141	C₄×D₄	—	4	8	no	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
144	C₂×C₂²⋊C₄	—	2	4	no	—
145	C₂×C₂²⋊C₄	—	2	2	no	—
146	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
147	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
148	C₂×C₄²	D₄×C₁₃	1	2	yes	—
149	C₂×C₄²	D₄×C₁₃	1	2	yes	—
150	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
151	C₄⋊C₈	—	2	4	no	—
152	#97	—	2	8	no	—
153	C₄×C₈	—	2	2	no	—
154	C₄×C₈	D₄×C₁₃	1	4	yes	complemented
155	C₂×C₁₃	—	8	4	no	—
156	C₂×C₁₃	#1484	1	2	yes	—
157	C₂×C₁₃	#1490	1	2	yes	—
158	C₂×C₁₃	#1955	1	1	yes	characteristic
159	C₂×C₁₃	#1961	1	1	yes	characteristic
160	C₂×C₁₃	#1962	1	1	yes	characteristic
161	C₂⁴	—	2	2	no	—
162	C₂×D₄	—	2	8	no	—
163	C₂×D₄	—	2	4	no	—
164	C₂×D₄	—	2	2	no	—
165	C₂×D₄	—	2	4	no	—
166	C₂×D₄	—	4	4	no	—
167	C₂×D₄	—	4	4	no	—
168	C₂×D₄	C₁₃×M₁₆	1	4	yes	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	4	2	no	—
171	C₂²×C₄	—	4	2	no	—
172	C₂²×C₄	—	4	8	no	—
173	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
174	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
175	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
176	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
177	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
178	C₂×C₈	—	2	8	no	—
179	C₂×C₈	—	2	4	no	—
180	C₂×C₈	—	4	2	no	—
181	C₂×C₈	—	4	4	no	—
182	C₄⋊C₄	—	2	4	no	—
183	C₄⋊C₄	—	4	4	no	—
184	C₂²⋊C₄	—	4	8	no	—
185	C₂²⋊C₄	—	4	4	no	—
186	C₄²	—	2	4	no	—
187	C₄²	—	2	2	no	—
188	C₄²	—	2	2	no	—
189	C₄²	—	2	4	no	—
190	C₄²	C₂×D₄×C₁₃	1	2	yes	—
191	C₄²	C₁₃×#41	1	2	yes	—
192	C₁₃	#9648	1	1	yes	characteristic, direct product factor, Sylow
193	C₂³	—	2	4	no	—
194	C₂³	—	4	2	no	—
195	C₂³	—	4	2	no	—
196	C₂³	—	4	4	no	—
197	C₂³	—	4	4	no	—
198	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
199	D₄	—	2	8	no	—
200	D₄	—	4	16	no	—
201	D₄	—	4	4	no	—
202	C₂×C₄	—	2	2	no	—
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	—	4	2	no	—
209	C₂×C₄	—	4	4	no	—
210	C₂×C₄	—	8	4	no	—
211	C₂×C₄	—	8	4	no	—
212	C₂×C₄	C₁₃×#104	1	4	yes	—
213	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
214	C₂×C₄	C₁₃×#121	1	2	yes	—
215	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
216	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
217	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
218	C₂×C₄	C₁₃×#131	1	2	yes	—
219	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
220	C₈	—	2	8	no	—
221	C₈	—	8	2	no	—
222	C₂²	—	4	8	no	—
223	C₂²	—	4	4	no	—
224	C₂²	—	8	4	no	—
225	C₂²	—	8	2	no	—
226	C₂²	—	8	2	no	—
227	C₂²	C₁₃×#390	1	1	yes	characteristic
228	C₂²	C₁₃×#407	1	1	yes	characteristic
229	C₂²	C₁₃×#408	1	1	yes	characteristic
230	C₂²	C₁₃×#418	1	2	yes	—
231	C₂²	C₂×C₁₃×#104	1	2	yes	—
232	C₄	—	2	4	no	—
233	C₄	—	2	2	no	—
234	C₄	—	4	2	no	—
235	C₄	—	8	2	no	—
236	C₄	C₁₃×#435	1	4	yes	—
237	C₄	C₁₃×#490	1	2	yes	—
238	C₄	C₁₃×#496	1	2	yes	—
239	C₂	—	8	4	no	—
240	C₂	C₁₃×#1484	1	2	yes	—
241	C₂	C₁₃×#1490	1	2	yes	—
242	C₂	C₁₃×#1955	1	1	yes	characteristic
243	C₂	C₁₃×#1961	1	1	yes	characteristic
244	C₂	C₁₃×#1962	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	C₂³×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂×C₁₃×#127	C₄
LCS	G ▷ C₂²×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
2. C₁₃×#1831	C₂	semidirect
3. C₄×C₁₃×#97	C₂	semidirect
4. C₂×C₁₃×D₄⋊C₈	C₂	semidirect
38. C₄×C₈×C₁₃	D₄	semidirect
39. #9648	C₁₃	direct (N × H)
72. #1831	C₂×C₁₃	semidirect
73. C₄×#97	C₂×C₁₃	semidirect
74. C₂×D₄⋊C₈	C₂×C₁₃	semidirect
154. C₄×C₈	D₄×C₁₃	semidirect
192. C₁₃	#9648	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₃×#127	2
C₁₃×#1831	2
C₄×C₁₃×#97	2
C₂×C₁₃×D₄⋊C₈	2
#9648	13

Subgroups — C13×#9648 #15695987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9648 #15695987