Subgroups — C₁₃×#12916 #15699255

Order 3328.

370 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3407	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2153	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2113	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1757	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1379	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
7	C₁₃×#504	—	2	4	no	—
8	C₂×C₁₃×M₃₂	—	2	2	no	—
9	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
11	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
12	C₁₃×#413	C₄	1	1	yes	characteristic
13	C₁₃×#410	C₄	1	1	yes	characteristic
14	C₁₃×#405	C₂²	1	2	yes	—
15	C₁₃×#364	—	2	4	no	—
16	C₁₃×C₂²⋊C₁₆	—	2	2	no	—
17	C₁₃×#344	C₄	1	2	yes	—
18	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
19	C₁₃×#131	—	2	2	no	—
20	C₁₃×#131	—	2	2	no	—
21	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
22	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
23	C₂×C₁₃×M₁₆	Q₈	1	2	yes	—
24	C₂²×C₈×C₁₃	D₄	1	2	yes	—
25	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
26	C₁₃×#117	C₂×C₄	1	2	yes	—
27	C₁₃×M₃₂	—	2	4	no	—
28	C₁₃×M₃₂	—	2	2	no	—
29	C₁₃×M₃₂	—	2	2	no	—
30	C₁₃×M₃₂	D₄	1	4	yes	—
31	C₂×C₁₃×C₁₆	—	2	4	no	—
32	C₂×C₁₃×C₁₆	—	2	2	no	—
33	C₂×C₁₃×C₁₆	—	2	1	no	—
34	C₂×C₁₃×C₁₆	—	2	1	no	—
35	C₂×C₁₃×C₁₆	—	2	2	no	—
36	C₁₃×#101	C₈	1	2	yes	—
37	C₁₃×#100	C₈	1	2	yes	—
38	C₁₃×#99	—	2	2	no	—
39	C₁₃×#97	—	2	2	no	—
40	C₄×C₈×C₁₃	—	2	2	no	—
41	#12916	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₁₃×#41	—	2	2	no	—
43	C₁₃×#41	—	2	2	no	—
44	C₂×Q₈×C₁₃	C₂×C₈	1	1	yes	characteristic
45	C₂×D₄×C₁₃	C₂×C₈	1	1	yes	characteristic
46	C₂×D₄×C₁₃	M₁₆	1	2	yes	—
47	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
48	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
49	C₁₃×M₁₆	—	2	2	no	—
50	C₁₃×M₁₆	—	2	2	no	—
51	C₁₃×M₁₆	—	2	4	no	—
52	C₁₃×M₁₆	C₂×C₈	1	4	yes	—
53	C₂×C₈×C₁₃	—	2	2	no	—
54	C₂×C₈×C₁₃	—	2	2	no	—
55	C₂×C₈×C₁₃	—	2	2	no	—
56	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
57	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
58	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
59	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
60	C₂×C₈×C₁₃	#41	1	2	yes	—
61	C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₁₃×C₂²⋊C₄	—	2	2	no	—
63	C₄²×C₁₃	—	2	2	no	—
64	C₁₃×C₁₆	—	2	4	no	—
65	C₁₃×C₁₆	—	4	1	no	—
66	C₁₃×C₁₆	—	4	1	no	—
67	#3407	C₂×C₁₃	1	1	yes	characteristic
68	#2153	C₂×C₁₃	1	2	yes	complemented
69	#2113	C₂×C₁₃	1	1	yes	characteristic
70	#1757	C₂×C₁₃	1	1	yes	characteristic
71	#1379	C₂×C₁₃	1	2	yes	complemented
72	C₂³×C₁₃	C₄⋊C₈	1	2	yes	—
73	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
74	Q₈×C₁₃	—	2	2	no	—
75	D₄×C₁₃	—	2	4	no	—
76	D₄×C₁₃	—	2	2	no	—
77	C₂×C₄×C₁₃	—	2	2	no	—
78	C₂×C₄×C₁₃	—	2	2	no	—
79	C₂×C₄×C₁₃	—	4	2	no	—
80	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
81	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
83	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
84	C₂×C₄×C₁₃	#131	1	2	yes	—
85	C₈×C₁₃	—	2	2	no	—
86	C₈×C₁₃	—	2	4	no	—
87	C₈×C₁₃	#120	1	1	yes	characteristic
88	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
89	C₈×C₁₃	#123	1	1	yes	characteristic
90	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
91	#504	—	2	4	no	—
92	C₂×M₃₂	—	2	2	no	—
93	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
94	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
95	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
96	#413	C₄×C₁₃	1	1	yes	characteristic
97	#410	C₄×C₁₃	1	1	yes	characteristic
98	#405	C₂²×C₁₃	1	2	yes	—
99	#364	—	2	4	no	—
100	C₂²⋊C₁₆	—	2	2	no	—
101	#344	C₄×C₁₃	1	2	yes	—
102	C₂²×C₁₃	—	2	2	no	—
103	C₂²×C₁₃	—	4	1	no	—
104	C₂²×C₁₃	—	4	2	no	—
105	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
106	C₂²×C₁₃	#435	1	2	yes	—
107	C₄×C₁₃	—	2	2	no	—
108	C₄×C₁₃	—	8	2	no	—
109	C₄×C₁₃	#385	1	1	yes	characteristic
110	C₄×C₁₃	#424	1	1	yes	characteristic
111	C₄×C₁₃	C₈×D₄	1	2	yes	—
112	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
113	#131	—	2	2	no	—
114	#131	—	2	2	no	—
115	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
116	C₂×M₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
117	C₂×M₁₆	Q₈×C₁₃	1	2	yes	—
118	C₂²×C₈	D₄×C₁₃	1	2	yes	—
119	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
120	#117	C₂×C₄×C₁₃	1	2	yes	—
121	M₃₂	—	2	4	no	—
122	M₃₂	—	2	2	no	—
123	M₃₂	—	2	2	no	—
124	M₃₂	D₄×C₁₃	1	4	yes	—
125	C₂×C₁₆	—	2	4	no	—
126	C₂×C₁₆	—	2	2	no	—
127	C₂×C₁₆	—	2	1	no	—
128	C₂×C₁₆	—	2	1	no	—
129	C₂×C₁₆	—	2	2	no	—
130	#101	C₈×C₁₃	1	2	yes	—
131	#100	C₈×C₁₃	1	2	yes	—
132	#99	—	2	2	no	—
133	#97	—	2	2	no	—
134	C₄×C₈	—	2	2	no	—
135	C₂×C₁₃	—	2	2	no	—
136	C₂×C₁₃	—	2	1	no	—
137	C₂×C₁₃	—	4	2	no	—
138	C₂×C₁₃	#1850	1	1	yes	characteristic
139	#41	—	2	2	no	—
140	#41	—	2	2	no	—
141	C₂×Q₈	C₂×C₈×C₁₃	1	1	yes	characteristic
142	C₂×D₄	C₂×C₈×C₁₃	1	1	yes	characteristic
143	C₂×D₄	C₁₃×M₁₆	1	2	yes	—
144	C₂²×C₄	C₁₃×C₄⋊C₄	1	2	yes	—
145	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
146	M₁₆	—	2	2	no	—
147	M₁₆	—	2	2	no	—
148	M₁₆	—	2	4	no	—
149	M₁₆	C₂×C₈×C₁₃	1	4	yes	—
150	C₂×C₈	—	2	2	no	—
151	C₂×C₈	—	2	2	no	—
152	C₂×C₈	—	2	2	no	—
153	C₂×C₈	C₁₃×C₄⋊C₄	1	2	yes	—
154	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
155	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
156	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
157	C₂×C₈	C₁₃×#41	1	2	yes	—
158	C₄⋊C₄	—	2	2	no	—
159	C₂²⋊C₄	—	2	2	no	—
160	C₄²	—	2	2	no	—
161	C₁₆	—	2	4	no	—
162	C₁₆	—	4	1	no	—
163	C₁₆	—	4	1	no	—
164	C₁₃	#12916	1	1	yes	characteristic, direct product factor, Sylow
165	C₂³	C₁₃×C₄⋊C₈	1	2	yes	—
166	C₂³	C₂×C₁₃×M₁₆	1	1	yes	characteristic
167	Q₈	—	2	2	no	—
168	D₄	—	2	4	no	—
169	D₄	—	2	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	4	2	no	—
173	C₂×C₄	C₁₃×C₄⋊C₈	1	2	yes	—
174	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
176	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
177	C₂×C₄	C₁₃×#131	1	2	yes	—
178	C₈	—	2	2	no	—
179	C₈	—	2	4	no	—
180	C₈	C₁₃×#120	1	1	yes	characteristic
181	C₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
182	C₈	C₁₃×#123	1	1	yes	characteristic
183	C₂²	—	2	2	no	—
184	C₂²	—	4	1	no	—
185	C₂²	—	4	2	no	—
186	C₂²	C₂×C₁₃×C₄⋊C₈	1	1	yes	characteristic
187	C₂²	C₁₃×#435	1	2	yes	—
188	C₄	—	2	2	no	—
189	C₄	—	8	2	no	—
190	C₄	C₁₃×#385	1	1	yes	characteristic
191	C₄	C₁₃×#424	1	1	yes	characteristic
192	C₄	C₈×D₄×C₁₃	1	2	yes	—
193	C₂	—	2	2	no	—
194	C₂	—	2	1	no	—
195	C₂	—	4	2	no	—
196	C₂	C₁₃×#1850	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₁₃	#120
commutator	C₂×C₄	C₂²×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#1850
prime radical	C₂×C₁₃×#41	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₃ ◁ C₂²×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2153	C₂	semidirect
5. C₁₃×#1379	C₂	semidirect
41. #12916	C₁₃	direct (N × H)
68. #2153	C₂×C₁₃	semidirect
71. #1379	C₂×C₁₃	semidirect
164. C₁₃	#12916	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×#3407	2
C₁₃×#2153	2
C₁₃×#2113	2
C₁₃×#1757	2
C₁₃×#1379	2
#12916	13

Subgroups — C13×#12916 #15699255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12916 #15699255