Subgroups — C₁₃×#9697 #15696036

Order 3328.

498 conjugacy classes of subgroups.

The subgroup lattice has 250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2862	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1842	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#333	C₂	1	2	yes	maximal
5	C₂×C₁₃×#332	C₂	1	2	yes	maximal
6	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
9	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
10	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
11	C₂×C₄×C₈×C₁₃	—	2	1	no	—
12	C₁₃×#391	—	2	1	no	—
13	C₁₃×#391	—	2	1	no	—
14	C₁₃×#391	C₄	1	4	yes	—
15	C₁₃×#382	—	2	2	no	—
16	C₄³×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#336	—	2	1	no	—
18	C₁₃×#333	—	2	4	no	—
19	C₁₃×#332	—	2	4	no	—
20	C₂²×Q₈×C₁₃	—	2	1	no	—
21	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
22	C₂²×C₈×C₁₃	—	2	2	no	—
23	C₂²×C₈×C₁₃	—	2	2	no	—
24	C₁₃×C₄⋊Q₈	—	2	2	no	—
25	C₁₃×C₄⋊Q₈	—	2	2	no	—
26	C₁₃×C₄⋊Q₈	—	2	2	no	—
27	C₁₃×C₄⋊Q₈	—	2	2	no	—
28	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
31	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
32	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
33	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₃	D₄	1	2	yes	—
36	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
37	C₁₃×C₄⋊C₈	—	2	2	no	—
38	C₁₃×C₄⋊C₈	—	2	2	no	—
39	C₁₃×C₄⋊C₈	—	2	2	no	—
40	C₁₃×C₄⋊C₈	—	4	4	no	—
41	C₁₃×C₄⋊C₈	D₄	1	4	yes	—
42	C₄×C₈×C₁₃	—	4	2	no	—
43	C₁₃×#95	—	2	4	no	—
44	C₁₃×#95	—	2	4	no	—
45	#9697	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×Q₈×C₁₃	—	2	4	no	—
47	C₂×Q₈×C₁₃	—	4	4	no	—
48	C₂×Q₈×C₁₃	—	4	2	no	—
49	C₂×Q₈×C₁₃	—	4	2	no	—
50	C₂×Q₈×C₁₃	—	4	1	no	—
51	C₂×Q₈×C₁₃	—	4	1	no	—
52	C₂²×C₄×C₁₃	—	2	2	no	—
53	C₂²×C₄×C₁₃	—	2	2	no	—
54	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
59	C₂×C₈×C₁₃	—	2	4	no	—
60	C₂×C₈×C₁₃	—	4	2	no	—
61	C₂×C₈×C₁₃	—	4	2	no	—
62	C₂×C₈×C₁₃	—	4	2	no	—
63	C₂×C₈×C₁₃	—	4	4	no	—
64	C₁₃×C₄⋊C₄	—	2	4	no	—
65	C₁₃×C₄⋊C₄	—	4	2	no	—
66	C₁₃×C₄⋊C₄	—	4	1	no	—
67	C₁₃×C₄⋊C₄	—	4	1	no	—
68	C₁₃×C₄⋊C₄	—	4	1	no	—
69	C₁₃×C₄⋊C₄	—	4	1	no	—
70	C₄²×C₁₃	—	2	2	no	—
71	C₄²×C₁₃	—	2	1	no	—
72	C₄²×C₁₃	—	2	1	no	—
73	C₄²×C₁₃	—	4	2	no	—
74	C₄²×C₁₃	SD₁₆	1	4	yes	—
75	C₄²×C₁₃	Q₁₆	1	4	yes	—
76	C₄²×C₁₃	C₂×D₄	1	2	yes	—
77	C₄²×C₁₃	#41	1	2	yes	—
78	#2862	C₂×C₁₃	1	1	yes	characteristic
79	#1842	C₂×C₁₃	1	1	yes	characteristic
80	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
81	C₂×#333	C₂×C₁₃	1	2	yes	—
82	C₂×#332	C₂×C₁₃	1	2	yes	—
83	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	Q₈×C₁₃	—	8	4	no	—
85	Q₈×C₁₃	—	8	2	no	—
86	Q₈×C₁₃	—	8	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	—	2	2	no	—
91	C₂×C₄×C₁₃	—	2	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	—	4	2	no	—
96	C₂×C₄×C₁₃	—	4	2	no	—
97	C₂×C₄×C₁₃	#103	1	4	yes	—
98	C₂×C₄×C₁₃	#103	1	4	yes	—
99	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
100	C₂×C₄×C₁₃	#121	1	2	yes	—
101	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
102	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
103	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
104	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
105	C₂×C₄×C₁₃	#135	1	2	yes	—
106	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
107	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
108	C₈×C₁₃	—	4	4	no	—
109	C₈×C₁₃	—	8	2	no	—
110	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
111	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
112	C₂×C₄⋊C₈	—	2	2	no	—
113	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
114	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
115	C₂×C₄×C₈	—	2	1	no	—
116	#391	—	2	1	no	—
117	#391	—	2	1	no	—
118	#391	C₄×C₁₃	1	4	yes	—
119	#382	—	2	2	no	—
120	C₄³	C₂²×C₁₃	1	1	yes	characteristic
121	#336	—	2	1	no	—
122	#333	—	2	4	no	—
123	#332	—	2	4	no	—
124	C₂²×C₁₃	#390	1	1	yes	characteristic
125	C₂²×C₁₃	#413	1	2	yes	—
126	C₂²×C₁₃	C₂×#103	1	2	yes	—
127	C₂²×C₁₃	#416	1	1	yes	characteristic
128	C₂²×C₁₃	#417	1	1	yes	characteristic
129	C₄×C₁₃	—	2	4	no	—
130	C₄×C₁₃	—	2	4	no	—
131	C₄×C₁₃	—	2	2	no	—
132	C₄×C₁₃	—	8	2	no	—
133	C₄×C₁₃	—	8	2	no	—
134	C₄×C₁₃	#463	1	2	yes	—
135	C₄×C₁₃	#464	1	2	yes	—
136	C₄×C₁₃	#487	1	2	yes	—
137	C₄×C₁₃	#492	1	1	yes	characteristic
138	C₄×C₁₃	#494	1	1	yes	characteristic
139	C₂²×Q₈	—	2	1	no	—
140	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
141	C₂²×C₈	—	2	2	no	—
142	C₂²×C₈	—	2	2	no	—
143	C₄⋊Q₈	—	2	2	no	—
144	C₄⋊Q₈	—	2	2	no	—
145	C₄⋊Q₈	—	2	2	no	—
146	C₄⋊Q₈	—	2	2	no	—
147	C₂×C₄⋊C₄	—	2	1	no	—
148	C₂×C₄⋊C₄	—	2	1	no	—
149	C₂×C₄⋊C₄	—	2	1	no	—
150	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
151	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
152	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
153	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
154	C₂×C₄²	D₄×C₁₃	1	2	yes	—
155	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
156	C₄⋊C₈	—	2	2	no	—
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	4	4	no	—
160	C₄⋊C₈	D₄×C₁₃	1	4	yes	—
161	C₄×C₈	—	4	2	no	—
162	#95	—	2	4	no	—
163	#95	—	2	4	no	—
164	C₂×C₁₃	#1542	1	2	yes	—
165	C₂×C₁₃	#1550	1	2	yes	—
166	C₂×C₁₃	#1956	1	1	yes	characteristic
167	C₂×C₁₃	#1967	1	1	yes	characteristic
168	C₂×C₁₃	#1983	1	1	yes	characteristic
169	C₂×Q₈	—	2	4	no	—
170	C₂×Q₈	—	4	4	no	—
171	C₂×Q₈	—	4	2	no	—
172	C₂×Q₈	—	4	2	no	—
173	C₂×Q₈	—	4	1	no	—
174	C₂×Q₈	—	4	1	no	—
175	C₂²×C₄	—	2	2	no	—
176	C₂²×C₄	—	2	2	no	—
177	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
178	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
179	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
180	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
181	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
182	C₂×C₈	—	2	4	no	—
183	C₂×C₈	—	4	2	no	—
184	C₂×C₈	—	4	2	no	—
185	C₂×C₈	—	4	2	no	—
186	C₂×C₈	—	4	4	no	—
187	C₄⋊C₄	—	2	4	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄⋊C₄	—	4	1	no	—
190	C₄⋊C₄	—	4	1	no	—
191	C₄⋊C₄	—	4	1	no	—
192	C₄⋊C₄	—	4	1	no	—
193	C₄²	—	2	2	no	—
194	C₄²	—	2	1	no	—
195	C₄²	—	2	1	no	—
196	C₄²	—	4	2	no	—
197	C₄²	C₁₃×SD₁₆	1	4	yes	—
198	C₄²	C₁₃×Q₁₆	1	4	yes	—
199	C₄²	C₂×D₄×C₁₃	1	2	yes	—
200	C₄²	C₁₃×#41	1	2	yes	—
201	C₁₃	#9697	1	1	yes	characteristic, direct product factor, Sylow
202	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
203	Q₈	—	8	4	no	—
204	Q₈	—	8	2	no	—
205	Q₈	—	8	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	4	2	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	—	4	4	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	C₁₃×#103	1	4	yes	—
217	C₂×C₄	C₁₃×#103	1	4	yes	—
218	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
219	C₂×C₄	C₁₃×#121	1	2	yes	—
220	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
221	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
222	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
223	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
224	C₂×C₄	C₁₃×#135	1	2	yes	—
225	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
226	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
227	C₈	—	4	4	no	—
228	C₈	—	8	2	no	—
229	C₂²	C₁₃×#390	1	1	yes	characteristic
230	C₂²	C₁₃×#413	1	2	yes	—
231	C₂²	C₂×C₁₃×#103	1	2	yes	—
232	C₂²	C₁₃×#416	1	1	yes	characteristic
233	C₂²	C₁₃×#417	1	1	yes	characteristic
234	C₄	—	2	4	no	—
235	C₄	—	2	4	no	—
236	C₄	—	2	2	no	—
237	C₄	—	8	2	no	—
238	C₄	—	8	2	no	—
239	C₄	C₁₃×#463	1	2	yes	—
240	C₄	C₁₃×#464	1	2	yes	—
241	C₄	C₁₃×#487	1	2	yes	—
242	C₄	C₁₃×#492	1	1	yes	characteristic
243	C₄	C₁₃×#494	1	1	yes	characteristic
244	C₂	C₁₃×#1542	1	2	yes	—
245	C₂	C₁₃×#1550	1	2	yes	—
246	C₂	C₁₃×#1956	1	1	yes	characteristic
247	C₂	C₁₃×#1967	1	1	yes	characteristic
248	C₂	C₁₃×#1983	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
45. #9697	C₁₃	direct (N × H)
201. C₁₃	#9697	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2862	2
C₁₃×#1842	2
C₄×C₁₃×C₄⋊C₈	2
C₂×C₁₃×#333	2
C₂×C₁₃×#332	2
#9697	13

Subgroups — C13×#9697 #15696036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9697 #15696036