Subgroups — C₈×C₁₃×#106 #15694619

Order 3328.

446 conjugacy classes of subgroups.

The subgroup lattice has 202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×#106	C₂	1	1	yes	maximal, characteristic
2	C₈×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal
3	C₂×C₁₃×#334	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈²×C₁₃	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1279	C₂	1	2	yes	maximal
6	C₂×C₁₃×#106	C₄	1	2	yes	—
7	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₁₃	—	2	2	no	—
9	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
13	C₁₃×#340	C₄	1	2	yes	—
14	C₁₃×#336	—	2	2	no	—
15	C₁₃×#334	C₄	1	4	yes	complemented
16	C₈²×C₁₃	C₄	1	4	yes	complemented
17	C₂²×C₈×C₁₃	—	2	1	no	—
18	C₂²×C₈×C₁₃	—	2	2	no	—
19	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
24	C₂×C₄²×C₁₃	—	2	2	no	—
25	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
26	C₁₃×#106	C₈	1	8	yes	direct product factor
27	C₁₃×C₄⋊C₈	—	2	2	no	—
28	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
29	C₄×C₈×C₁₃	—	2	1	no	—
30	C₄×C₈×C₁₃	—	4	4	no	—
31	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
32	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
33	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
34	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
35	C₄×C₈×C₁₃	Q₈	1	2	yes	—
36	C₁₃×#95	—	2	2	no	—
37	C₈×#106	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂²×C₄×C₁₃	—	2	4	no	—
39	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
42	C₂×C₈×C₁₃	—	2	4	no	—
43	C₂×C₈×C₁₃	—	2	2	no	—
44	C₂×C₈×C₁₃	—	2	2	no	—
45	C₂×C₈×C₁₃	—	2	2	no	—
46	C₂×C₈×C₁₃	—	2	4	no	—
47	C₂×C₈×C₁₃	—	4	2	no	—
48	C₂×C₈×C₁₃	—	4	2	no	—
49	C₂×C₈×C₁₃	C₄²	1	2	yes	—
50	C₂×C₈×C₁₃	C₄²	1	2	yes	—
51	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
52	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
53	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
54	C₂×C₈×C₁₃	SD₁₆	1	4	yes	—
55	C₁₃×C₄⋊C₄	—	2	4	no	—
56	C₁₃×C₄⋊C₄	C₂×C₈	1	8	yes	—
57	C₄²×C₁₃	—	4	2	no	—
58	C₄²×C₁₃	—	4	2	no	—
59	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
60	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
61	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
62	C₄²×C₁₃	#41	1	1	yes	characteristic
63	C₄×#106	C₂×C₁₃	1	1	yes	characteristic
64	C₈×C₄⋊C₄	C₂×C₁₃	1	2	yes	—
65	C₂×#334	C₂×C₁₃	1	1	yes	characteristic
66	C₂×C₈²	C₂×C₁₃	1	1	yes	characteristic
67	#1279	C₂×C₁₃	1	2	yes	—
68	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
69	C₂×C₄×C₁₃	—	2	2	no	—
70	C₂×C₄×C₁₃	—	2	8	no	—
71	C₂×C₄×C₁₃	—	4	4	no	—
72	C₂×C₄×C₁₃	—	4	4	no	—
73	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
74	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
75	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
76	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
77	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
80	C₂×C₄×C₁₃	#131	1	2	yes	—
81	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
82	C₂×C₄×C₁₃	#135	1	2	yes	—
83	C₈×C₁₃	—	2	4	no	—
84	C₈×C₁₃	—	2	2	no	—
85	C₈×C₁₃	—	2	2	no	—
86	C₈×C₁₃	—	4	4	no	—
87	C₈×C₁₃	C₄×C₈	1	4	yes	complemented
88	C₈×C₁₃	#106	1	4	yes	direct product factor
89	C₂×#106	C₄×C₁₃	1	2	yes	—
90	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
91	C₂×C₄×C₈	—	2	2	no	—
92	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
93	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
94	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
95	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
96	#340	C₄×C₁₃	1	2	yes	—
97	#336	—	2	2	no	—
98	#334	C₄×C₁₃	1	4	yes	complemented
99	C₈²	C₄×C₁₃	1	4	yes	complemented
100	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
101	C₂²×C₁₃	C₈×D₄	1	2	yes	—
102	C₂²×C₁₃	C₄×SD₁₆	1	2	yes	—
103	C₂²×C₁₃	#443	1	2	yes	—
104	C₄×C₁₃	—	2	1	no	—
105	C₄×C₁₃	—	2	1	no	—
106	C₄×C₁₃	—	4	8	no	—
107	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
108	C₄×C₁₃	#405	1	1	yes	characteristic
109	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
110	C₄×C₁₃	#427	1	1	yes	characteristic
111	C₄×C₁₃	C₄×SD₁₆	1	2	yes	—
112	C₄×C₁₃	C₈×Q₈	1	2	yes	—
113	C₂²×C₈	—	2	1	no	—
114	C₂²×C₈	—	2	2	no	—
115	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
116	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
117	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
118	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
119	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
120	C₂×C₄²	—	2	2	no	—
121	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
122	#106	C₈×C₁₃	1	8	yes	direct product factor
123	C₄⋊C₈	—	2	2	no	—
124	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
125	C₄×C₈	—	2	1	no	—
126	C₄×C₈	—	4	4	no	—
127	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
128	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
129	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
130	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
131	C₄×C₈	Q₈×C₁₃	1	2	yes	—
132	#95	—	2	2	no	—
133	C₂×C₁₃	C₈×SD₁₆	1	4	yes	—
134	C₂×C₁₃	C₈×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₁₃	#1772	1	1	yes	characteristic
136	C₂×C₁₃	C₄×#106	1	1	yes	characteristic
137	C₂²×C₄	—	2	4	no	—
138	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
139	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
140	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
141	C₂×C₈	—	2	4	no	—
142	C₂×C₈	—	2	2	no	—
143	C₂×C₈	—	2	2	no	—
144	C₂×C₈	—	2	2	no	—
145	C₂×C₈	—	2	4	no	—
146	C₂×C₈	—	4	2	no	—
147	C₂×C₈	—	4	2	no	—
148	C₂×C₈	C₄²×C₁₃	1	2	yes	—
149	C₂×C₈	C₄²×C₁₃	1	2	yes	—
150	C₂×C₈	C₁₃×C₄⋊C₄	1	2	yes	—
151	C₂×C₈	C₁₃×C₄⋊C₄	1	2	yes	—
152	C₂×C₈	C₂×C₈×C₁₃	1	4	yes	—
153	C₂×C₈	C₁₃×SD₁₆	1	4	yes	—
154	C₄⋊C₄	—	2	4	no	—
155	C₄⋊C₄	C₂×C₈×C₁₃	1	8	yes	—
156	C₄²	—	4	2	no	—
157	C₄²	—	4	2	no	—
158	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
159	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
160	C₄²	C₂×Q₈×C₁₃	1	1	yes	characteristic
161	C₄²	C₁₃×#41	1	1	yes	characteristic
162	C₁₃	C₈×#106	1	1	yes	characteristic, direct product factor, Sylow
163	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	8	no	—
166	C₂×C₄	—	4	4	no	—
167	C₂×C₄	—	4	4	no	—
168	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
169	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄	C₁₃×#117	1	1	yes	characteristic
171	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
172	C₂×C₄	C₄×Q₈×C₁₃	1	1	yes	characteristic
173	C₂×C₄	C₄×Q₈×C₁₃	1	1	yes	characteristic
174	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
175	C₂×C₄	C₁₃×#131	1	2	yes	—
176	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
177	C₂×C₄	C₁₃×#135	1	2	yes	—
178	C₈	—	2	4	no	—
179	C₈	—	2	2	no	—
180	C₈	—	2	2	no	—
181	C₈	—	4	4	no	—
182	C₈	C₄×C₈×C₁₃	1	4	yes	complemented
183	C₈	C₁₃×#106	1	4	yes	direct product factor
184	C₂²	C₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
185	C₂²	C₈×D₄×C₁₃	1	2	yes	—
186	C₂²	C₄×C₁₃×SD₁₆	1	2	yes	—
187	C₂²	C₁₃×#443	1	2	yes	—
188	C₄	—	2	1	no	—
189	C₄	—	2	1	no	—
190	C₄	—	4	8	no	—
191	C₄	C₂×C₄×C₈×C₁₃	1	1	yes	characteristic
192	C₄	C₁₃×#405	1	1	yes	characteristic
193	C₄	C₂×C₁₃×#106	1	1	yes	characteristic
194	C₄	C₁₃×#427	1	1	yes	characteristic
195	C₄	C₄×C₁₃×SD₁₆	1	2	yes	—
196	C₄	C₈×Q₈×C₁₃	1	2	yes	—
197	C₂	C₈×C₁₃×SD₁₆	1	4	yes	—
198	C₂	C₈×C₁₃×C₄⋊C₄	1	1	yes	characteristic
199	C₂	C₁₃×#1772	1	1	yes	characteristic
200	C₂	C₄×C₁₃×#106	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈×C₁₃	D₄
commutator	C₄	C₂×C₄×C₈×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle, prime radical	C₂³×C₁₃	C₄×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₁₃×#334	C₄	semidirect
16. C₈²×C₁₃	C₄	semidirect
26. C₁₃×#106	C₈	direct (N × H)
37. C₈×#106	C₁₃	direct (N × H)
87. C₈×C₁₃	C₄×C₈	semidirect
88. C₈×C₁₃	#106	direct (N × H)
98. #334	C₄×C₁₃	semidirect
99. C₈²	C₄×C₁₃	semidirect
122. #106	C₈×C₁₃	direct (N × H)
162. C₁₃	C₈×#106	direct (N × H)
182. C₈	C₄×C₈×C₁₃	semidirect
183. C₈	C₁₃×#106	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×#106	2
C₈×C₁₃×C₄⋊C₄	2
C₂×C₁₃×#334	2
C₂×C₈²×C₁₃	2
C₁₃×#1279	2
C₈×#106	13

Subgroups — C8×C13×#106 #15694619

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₁₃×#106 #15694619