Subgroups — C₁₃×#9623 #15695962

Order 3328.

298 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#1950	C₂	1	2	yes	maximal
2	C₁₃×#1566	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#334	C₂	1	1	yes	maximal, characteristic
4	C₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1301	C₂	1	2	yes	maximal
6	C₁₃×#431	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×#108	—	2	2	no	—
8	C₁₃×#423	C₂²	1	2	yes	—
9	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
10	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#341	—	2	2	no	—
13	C₁₃×#334	—	2	1	no	—
14	C₁₃×#334	—	2	1	no	—
15	C₁₃×#334	C₄	1	2	yes	—
16	C₁₃×#334	C₄	1	2	yes	—
17	C₁₃×#322	—	2	1	no	—
18	C₈²×C₁₃	—	2	1	no	—
19	C₂×C₁₃×M₁₆	—	2	2	no	—
20	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
21	C₂²×C₈×C₁₃	—	2	2	no	—
22	C₂²×C₈×C₁₃	Q₈	1	1	yes	characteristic
23	C₂²×C₈×C₁₃	Q₈	1	1	yes	characteristic
24	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
25	C₁₃×#108	—	4	4	no	—
26	C₁₃×C₄⋊C₈	—	2	2	no	—
27	C₁₃×C₄⋊C₈	—	2	2	no	—
28	C₁₃×C₄⋊C₈	—	2	1	no	—
29	C₁₃×C₄⋊C₈	—	2	2	no	—
30	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
31	C₁₃×C₂²⋊C₈	Q₈	1	2	yes	—
32	C₁₃×#97	—	2	1	no	—
33	C₄×C₈×C₁₃	—	2	1	no	—
34	C₄×C₈×C₁₃	—	2	1	no	—
35	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
38	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
39	#9623	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
43	C₁₃×M₁₆	—	2	2	no	—
44	C₁₃×M₁₆	—	4	2	no	—
45	C₁₃×M₁₆	—	4	2	no	—
46	C₁₃×M₁₆	SD₁₆	1	4	yes	—
47	C₂×C₈×C₁₃	—	2	2	no	—
48	C₂×C₈×C₁₃	—	2	2	no	—
49	C₂×C₈×C₁₃	—	2	4	no	—
50	C₂×C₈×C₁₃	—	2	2	no	—
51	C₂×C₈×C₁₃	—	4	1	no	—
52	C₂×C₈×C₁₃	—	4	2	no	—
53	C₂×C₈×C₁₃	—	4	2	no	—
54	C₂×C₈×C₁₃	—	4	2	no	—
55	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
56	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
57	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
59	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
60	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
61	C₄²×C₁₃	#41	1	1	yes	characteristic
62	C₄²×C₁₃	#41	1	1	yes	characteristic
63	#1950	C₂×C₁₃	1	2	yes	—
64	#1566	C₂×C₁₃	1	1	yes	characteristic
65	C₂×#334	C₂×C₁₃	1	1	yes	characteristic
66	C₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic
67	#1301	C₂×C₁₃	1	2	yes	—
68	C₂³×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
69	C₂×C₄×C₁₃	—	2	1	no	—
70	C₂×C₄×C₁₃	—	2	1	no	—
71	C₂×C₄×C₁₃	—	4	1	no	—
72	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
74	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
75	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
76	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
77	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
79	C₂×C₄×C₁₃	#135	1	2	yes	—
80	C₈×C₁₃	—	2	1	no	—
81	C₈×C₁₃	—	2	1	no	—
82	C₈×C₁₃	—	2	1	no	—
83	C₈×C₁₃	—	2	4	no	—
84	C₈×C₁₃	—	4	2	no	—
85	C₈×C₁₃	—	4	4	no	—
86	C₈×C₁₃	—	8	2	no	—
87	C₈×C₁₃	#108	1	2	yes	complemented
88	#431	C₂²×C₁₃	1	1	yes	characteristic
89	C₂×#108	—	2	2	no	—
90	#423	C₂²×C₁₃	1	2	yes	—
91	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
92	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
93	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
94	#341	—	2	2	no	—
95	#334	—	2	1	no	—
96	#334	—	2	1	no	—
97	#334	C₄×C₁₃	1	2	yes	—
98	#334	C₄×C₁₃	1	2	yes	—
99	#322	—	2	1	no	—
100	C₈²	—	2	1	no	—
101	C₂²×C₁₃	—	2	1	no	—
102	C₂²×C₁₃	—	2	1	no	—
103	C₂²×C₁₃	#389	1	1	yes	characteristic
104	C₂²×C₁₃	#498	1	1	yes	characteristic
105	C₂²×C₁₃	#499	1	1	yes	characteristic
106	C₄×C₁₃	—	2	1	no	—
107	C₄×C₁₃	—	2	1	no	—
108	C₄×C₁₃	—	2	1	no	—
109	C₄×C₁₃	C₂×#108	1	1	yes	characteristic
110	C₄×C₁₃	#430	1	1	yes	characteristic
111	C₄×C₁₃	C₄×SD₁₆	1	2	yes	—
112	C₄×C₁₃	#465	1	2	yes	—
113	C₂×M₁₆	—	2	2	no	—
114	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
115	C₂²×C₈	—	2	2	no	—
116	C₂²×C₈	Q₈×C₁₃	1	1	yes	characteristic
117	C₂²×C₈	Q₈×C₁₃	1	1	yes	characteristic
118	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
119	#108	—	4	4	no	—
120	C₄⋊C₈	—	2	2	no	—
121	C₄⋊C₈	—	2	2	no	—
122	C₄⋊C₈	—	2	1	no	—
123	C₄⋊C₈	—	2	2	no	—
124	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
125	C₂²⋊C₈	Q₈×C₁₃	1	2	yes	—
126	#97	—	2	1	no	—
127	C₄×C₈	—	2	1	no	—
128	C₄×C₈	—	2	1	no	—
129	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
130	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
131	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
132	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
133	C₂×C₁₃	—	2	1	no	—
134	C₂×C₁₃	—	2	1	no	—
135	C₂×C₁₃	#1941	1	1	yes	characteristic
136	C₂×C₁₃	#1950	1	1	yes	characteristic
137	C₂×C₁₃	#1953	1	1	yes	characteristic
138	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
139	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
140	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
141	M₁₆	—	2	2	no	—
142	M₁₆	—	4	2	no	—
143	M₁₆	—	4	2	no	—
144	M₁₆	C₁₃×SD₁₆	1	4	yes	—
145	C₂×C₈	—	2	2	no	—
146	C₂×C₈	—	2	2	no	—
147	C₂×C₈	—	2	4	no	—
148	C₂×C₈	—	2	2	no	—
149	C₂×C₈	—	4	1	no	—
150	C₂×C₈	—	4	2	no	—
151	C₂×C₈	—	4	2	no	—
152	C₂×C₈	—	4	2	no	—
153	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
157	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
158	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
159	C₄²	C₁₃×#41	1	1	yes	characteristic
160	C₄²	C₁₃×#41	1	1	yes	characteristic
161	C₁₃	#9623	1	1	yes	characteristic, direct product factor, Sylow
162	C₂³	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	4	1	no	—
166	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
168	C₂×C₄	C₄×Q₈×C₁₃	1	1	yes	characteristic
169	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
170	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
171	C₂×C₄	C₁₃×#125	1	1	yes	characteristic
172	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
173	C₂×C₄	C₁₃×#135	1	2	yes	—
174	C₈	—	2	1	no	—
175	C₈	—	2	1	no	—
176	C₈	—	2	1	no	—
177	C₈	—	2	4	no	—
178	C₈	—	4	2	no	—
179	C₈	—	4	4	no	—
180	C₈	—	8	2	no	—
181	C₈	C₁₃×#108	1	2	yes	complemented
182	C₂²	—	2	1	no	—
183	C₂²	—	2	1	no	—
184	C₂²	C₁₃×#389	1	1	yes	characteristic
185	C₂²	C₁₃×#498	1	1	yes	characteristic
186	C₂²	C₁₃×#499	1	1	yes	characteristic
187	C₄	—	2	1	no	—
188	C₄	—	2	1	no	—
189	C₄	—	2	1	no	—
190	C₄	C₂×C₁₃×#108	1	1	yes	characteristic
191	C₄	C₁₃×#430	1	1	yes	characteristic
192	C₄	C₄×C₁₃×SD₁₆	1	2	yes	—
193	C₄	C₁₃×#465	1	2	yes	—
194	C₂	—	2	1	no	—
195	C₂	—	2	1	no	—
196	C₂	C₁₃×#1941	1	1	yes	characteristic
197	C₂	C₁₃×#1950	1	1	yes	characteristic
198	C₂	C₁₃×#1953	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	#121
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle	C₂²×C₁₃	#389
prime radical	C₂³×C₁₃	C₄⋊Q₈
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
39. #9623	C₁₃	direct (N × H)
87. C₈×C₁₃	#108	semidirect
161. C₁₃	#9623	direct (N × H)
181. C₈	C₁₃×#108	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#1950	2
C₁₃×#1566	2
C₂×C₁₃×#334	2
C₈×C₁₃×M₁₆	2
C₁₃×#1301	2
#9623	13

Subgroups — C13×#9623 #15695962

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9623 #15695962