Subgroups — C₁₃×#13163 #15699502

Order 3328.

318 conjugacy classes of subgroups.

The subgroup lattice has 226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#364	C₂	1	2	yes	maximal
2	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
4	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1376	C₂	1	2	yes	maximal
6	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
7	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
13	C₁₃×#364	—	2	4	no	—
14	C₁₃×C₄⋊C₁₆	—	2	1	no	—
15	C₁₃×C₄⋊C₁₆	—	2	1	no	—
16	C₁₃×#346	—	2	1	no	—
17	C₄×C₁₃×C₁₆	—	2	1	no	—
18	C₁₃×#336	C₄	1	2	yes	—
19	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
21	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
23	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₁₃×M₃₂	—	2	1	no	—
26	C₁₃×M₃₂	—	2	1	no	—
27	C₁₃×M₃₂	—	2	2	no	—
28	C₁₃×M₃₂	—	2	2	no	—
29	C₁₃×M₃₂	D₄	1	2	yes	—
30	C₁₃×M₃₂	Q₈	1	2	yes	—
31	C₂×C₁₃×C₁₆	—	2	1	no	—
32	C₂×C₁₃×C₁₆	—	2	1	no	—
33	C₂×C₁₃×C₁₆	—	2	2	no	—
34	C₁₃×C₄⋊C₈	C₈	1	2	yes	—
35	C₁₃×C₄⋊C₈	C₈	1	2	yes	—
36	C₄×C₈×C₁₃	—	2	2	no	—
37	C₄×C₈×C₁₃	—	2	2	no	—
38	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
39	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
40	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
41	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
42	C₁₃×#95	—	2	1	no	—
43	#13163	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₄×C₁₃	—	2	2	no	—
45	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
46	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₈×C₁₃	—	2	2	no	—
49	C₂×C₈×C₁₃	—	2	1	no	—
50	C₂×C₈×C₁₃	—	2	1	no	—
51	C₂×C₈×C₁₃	—	2	2	no	—
52	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
54	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
55	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
56	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
57	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
58	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
59	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
60	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
61	C₁₃×C₄⋊C₄	—	2	4	no	—
62	C₄²×C₁₃	—	2	2	no	—
63	C₄²×C₁₃	—	2	2	no	—
64	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
65	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
66	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
67	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
68	C₁₃×C₁₆	—	2	2	no	—
69	C₁₃×C₁₆	—	2	2	no	—
70	C₁₃×C₁₆	—	4	2	no	—
71	C₂×#364	C₂×C₁₃	1	2	yes	—
72	#2150	C₂×C₁₃	1	1	yes	characteristic
73	C₄×M₃₂	C₂×C₁₃	1	1	yes	characteristic
74	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
75	#1376	C₂×C₁₃	1	2	yes	—
76	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
77	C₂×C₄×C₁₃	—	2	2	no	—
78	C₂×C₄×C₁₃	—	2	4	no	—
79	C₂×C₄×C₁₃	—	4	1	no	—
80	C₂×C₄×C₁₃	—	4	2	no	—
81	C₂×C₄×C₁₃	—	4	2	no	—
82	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
83	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
84	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
85	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
86	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
88	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
89	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
90	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
91	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
92	C₈×C₁₃	—	2	1	no	—
93	C₈×C₁₃	—	2	1	no	—
94	C₈×C₁₃	—	2	4	no	—
95	C₈×C₁₃	#121	1	1	yes	characteristic
96	C₈×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
97	C₈×C₁₃	#125	1	1	yes	characteristic
98	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
99	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
100	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
101	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
102	C₂×C₄⋊C₈	C₄×C₁₃	1	1	yes	characteristic
103	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
104	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
105	C₄×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
106	#364	—	2	4	no	—
107	C₄⋊C₁₆	—	2	1	no	—
108	C₄⋊C₁₆	—	2	1	no	—
109	#346	—	2	1	no	—
110	C₄×C₁₆	—	2	1	no	—
111	#336	C₄×C₁₃	1	2	yes	—
112	C₂²×C₁₃	—	2	1	no	—
113	C₂²×C₁₃	—	2	1	no	—
114	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
115	C₂²×C₁₃	#436	1	1	yes	characteristic
116	C₂²×C₁₃	#446	1	1	yes	characteristic
117	C₄×C₁₃	—	2	1	no	—
118	C₄×C₁₃	—	2	1	no	—
119	C₄×C₁₃	—	2	1	no	—
120	C₄×C₁₃	—	4	4	no	—
121	C₄×C₁₃	#364	1	2	yes	complemented
122	C₄×C₁₃	#389	1	1	yes	characteristic
123	C₄×C₁₃	#424	1	1	yes	characteristic
124	C₄×C₁₃	C₈×D₄	1	1	yes	characteristic
125	C₄×C₁₃	C₈×Q₈	1	1	yes	characteristic
126	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
127	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
128	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
129	C₂×C₄⋊C₄	—	2	1	no	—
130	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
131	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
132	M₃₂	—	2	1	no	—
133	M₃₂	—	2	1	no	—
134	M₃₂	—	2	2	no	—
135	M₃₂	—	2	2	no	—
136	M₃₂	D₄×C₁₃	1	2	yes	—
137	M₃₂	Q₈×C₁₃	1	2	yes	—
138	C₂×C₁₆	—	2	1	no	—
139	C₂×C₁₆	—	2	1	no	—
140	C₂×C₁₆	—	2	2	no	—
141	C₄⋊C₈	C₈×C₁₃	1	2	yes	—
142	C₄⋊C₈	C₈×C₁₃	1	2	yes	—
143	C₄×C₈	—	2	2	no	—
144	C₄×C₈	—	2	2	no	—
145	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
146	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
147	C₄×C₈	Q₈×C₁₃	1	1	yes	characteristic
148	C₄×C₈	Q₈×C₁₃	1	1	yes	characteristic
149	#95	—	2	1	no	—
150	C₂×C₁₃	—	2	1	no	—
151	C₂×C₁₃	—	2	1	no	—
152	C₂×C₁₃	#1939	1	1	yes	characteristic
153	C₂×C₁₃	C₂×#364	1	1	yes	characteristic
154	C₂×C₁₃	#2153	1	1	yes	characteristic
155	C₂²×C₄	—	2	2	no	—
156	C₂²×C₄	C₁₃×M₁₆	1	1	yes	characteristic
157	C₂²×C₄	C₁₃×M₁₆	1	1	yes	characteristic
158	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
159	C₂×C₈	—	2	2	no	—
160	C₂×C₈	—	2	1	no	—
161	C₂×C₈	—	2	1	no	—
162	C₂×C₈	—	2	2	no	—
163	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₈	C₂×C₈×C₁₃	1	4	yes	—
166	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
167	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
168	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
169	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
170	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
171	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
172	C₄⋊C₄	—	2	4	no	—
173	C₄²	—	2	2	no	—
174	C₄²	—	2	2	no	—
175	C₄²	C₁₃×C₄⋊C₄	1	1	yes	characteristic
176	C₄²	C₁₃×C₄⋊C₄	1	1	yes	characteristic
177	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
178	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
179	C₁₆	—	2	2	no	—
180	C₁₆	—	2	2	no	—
181	C₁₆	—	4	2	no	—
182	C₁₃	#13163	1	1	yes	characteristic, direct product factor, Sylow
183	C₂³	C₂×C₁₃×M₁₆	1	1	yes	characteristic
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	2	4	no	—
186	C₂×C₄	—	4	1	no	—
187	C₂×C₄	—	4	2	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	C₁₃×C₄⋊C₈	1	1	yes	characteristic
190	C₂×C₄	C₁₃×C₄⋊C₈	1	1	yes	characteristic
191	C₂×C₄	C₁₃×C₄⋊C₈	1	1	yes	characteristic
192	C₂×C₄	C₁₃×C₄⋊C₈	1	1	yes	characteristic
193	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
194	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
195	C₂×C₄	C₄×Q₈×C₁₃	1	1	yes	characteristic
196	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
197	C₂×C₄	C₁₃×#131	1	1	yes	characteristic
198	C₂×C₄	C₁₃×#131	1	1	yes	characteristic
199	C₈	—	2	1	no	—
200	C₈	—	2	1	no	—
201	C₈	—	2	4	no	—
202	C₈	C₁₃×#121	1	1	yes	characteristic
203	C₈	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
204	C₈	C₁₃×#125	1	1	yes	characteristic
205	C₈	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
206	C₂²	—	2	1	no	—
207	C₂²	—	2	1	no	—
208	C₂²	C₂×C₁₃×C₄⋊C₈	1	1	yes	characteristic
209	C₂²	C₁₃×#436	1	1	yes	characteristic
210	C₂²	C₁₃×#446	1	1	yes	characteristic
211	C₄	—	2	1	no	—
212	C₄	—	2	1	no	—
213	C₄	—	2	1	no	—
214	C₄	—	4	4	no	—
215	C₄	C₁₃×#364	1	2	yes	complemented
216	C₄	C₁₃×#389	1	1	yes	characteristic
217	C₄	C₁₃×#424	1	1	yes	characteristic
218	C₄	C₈×D₄×C₁₃	1	1	yes	characteristic
219	C₄	C₈×Q₈×C₁₃	1	1	yes	characteristic
220	C₂	—	2	1	no	—
221	C₂	—	2	1	no	—
222	C₂	C₁₃×#1939	1	1	yes	characteristic
223	C₂	C₂×C₁₃×#364	1	1	yes	characteristic
224	C₂	C₁₃×#2153	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×C₄⋊C₈
prime radical	C₂³×C₁₃	C₂×M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
43. #13163	C₁₃	direct (N × H)
121. C₄×C₁₃	#364	semidirect
182. C₁₃	#13163	direct (N × H)
215. C₄	C₁₃×#364	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#364	2
C₁₃×#2150	2
C₄×C₁₃×M₃₂	2
C₈×C₁₃×C₄⋊C₄	2
C₁₃×#1376	2
#13163	13

Subgroups — C13×#13163 #15699502

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13163 #15699502