Subgroups — C₁₃×#17316 #15703655

Order 3328.

890 conjugacy classes of subgroups.

The subgroup lattice has 156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₁₃×#41	C₂	1	2	yes	maximal
2	C₄×C₁₃×#131	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1450	C₂	1	3	yes	maximal, complemented
4	C₈×C₁₃×M₁₆	C₂	1	6	yes	maximal, complemented
5	C₂×C₁₃×#322	C₂	1	3	yes	maximal, complemented
6	C₂×C₁₃×#131	C₄	1	2	yes	—
7	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
8	C₈×Q₈×C₁₃	C₄	1	4	yes	—
9	C₈×D₄×C₁₃	C₄	1	12	yes	—
10	C₁₃×#431	C₂²	1	6	yes	—
11	C₁₃×#405	C₄	1	6	yes	—
12	C₄×C₁₃×M₁₆	C₂²	1	3	yes	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
14	C₂×C₄×C₈×C₁₃	C₂²	1	6	yes	—
15	C₁₃×#322	C₂²	1	1	yes	characteristic
16	C₁₃×#322	C₂²	1	6	yes	—
17	C₁₃×#322	C₂²	1	3	yes	—
18	C₈²×C₁₃	C₂²	1	6	yes	—
19	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
20	C₁₃×#131	C₈	1	16	yes	complemented
21	C₂×C₁₃×M₁₆	C₂×C₄	1	6	yes	—
22	C₂²×C₈×C₁₃	C₂×C₄	1	12	yes	—
23	C₂²×C₈×C₁₃	C₂×C₄	1	6	yes	—
24	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
25	C₄×D₄×C₁₃	C₂×C₄	1	6	yes	—
26	C₁₃×#117	C₂×C₄	1	3	yes	—
27	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
28	C₁₃×C₄⋊C₈	C₂×C₄	1	12	yes	—
29	C₁₃×C₂²⋊C₈	C₂×C₄	1	12	yes	—
30	C₁₃×#97	C₂×C₄	1	6	yes	—
31	C₄×C₈×C₁₃	C₂×C₄	1	6	yes	—
32	C₄×C₈×C₁₃	C₂×C₄	1	12	yes	—
33	C₄×C₈×C₁₃	C₂³	1	3	yes	—
34	C₄×C₈×C₁₃	C₂³	1	6	yes	—
35	C₄×C₈×C₁₃	C₂³	1	2	yes	—
36	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
37	#17316	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₁₃×#41	C₂×C₈	1	8	yes	—
39	C₂×Q₈×C₁₃	C₄²	1	1	yes	characteristic
40	C₂×D₄×C₁₃	C₄²	1	3	yes	—
41	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
42	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
43	C₁₃×M₁₆	C₂×C₈	1	24	yes	complemented
44	C₂×C₈×C₁₃	—	4	12	no	—
45	C₂×C₈×C₁₃	C₂×C₈	1	24	yes	complemented
46	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
47	C₂×C₈×C₁₃	C₂²×C₄	1	12	yes	—
48	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
49	C₂×C₈×C₁₃	C₂²×C₄	1	6	yes	—
50	C₁₃×C₄⋊C₄	C₄²	1	6	yes	—
51	C₁₃×C₂²⋊C₄	C₄²	1	6	yes	—
52	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
53	C₄²×C₁₃	C₂²×C₄	1	6	yes	—
54	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
55	C₈×#41	C₂×C₁₃	1	2	yes	—
56	C₄×#131	C₂×C₁₃	1	1	yes	characteristic
57	#1450	C₂×C₁₃	1	3	yes	complemented
58	C₈×M₁₆	C₂×C₁₃	1	6	yes	complemented
59	C₂×#322	C₂×C₁₃	1	3	yes	complemented
60	C₂³×C₁₃	C₂×C₄²	1	3	yes	—
61	Q₈×C₁₃	C₄×C₈	1	4	yes	—
62	D₄×C₁₃	C₄×C₈	1	12	yes	—
63	C₂×C₄×C₁₃	—	2	12	no	—
64	C₂×C₄×C₁₃	C₂×C₄²	1	6	yes	—
65	C₂×C₄×C₁₃	C₂×C₄²	1	3	yes	—
66	C₂×C₄×C₁₃	C₂²×C₈	1	12	yes	—
67	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
68	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
69	C₈×C₁₃	—	2	4	no	—
70	C₈×C₁₃	—	2	12	no	—
71	C₈×C₁₃	C₂²×C₈	1	4	yes	—
72	C₈×C₁₃	C₂²×C₈	1	12	yes	—
73	C₂×#131	C₄×C₁₃	1	2	yes	—
74	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
75	C₈×Q₈	C₄×C₁₃	1	4	yes	—
76	C₈×D₄	C₄×C₁₃	1	12	yes	—
77	#431	C₂²×C₁₃	1	6	yes	—
78	#405	C₄×C₁₃	1	6	yes	—
79	C₄×M₁₆	C₂²×C₁₃	1	3	yes	—
80	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	—
81	C₂×C₄×C₈	C₂²×C₁₃	1	6	yes	—
82	#322	C₂²×C₁₃	1	1	yes	characteristic
83	#322	C₂²×C₁₃	1	6	yes	—
84	#322	C₂²×C₁₃	1	3	yes	—
85	C₈²	C₂²×C₁₃	1	6	yes	—
86	C₂²×C₁₃	—	2	6	no	—
87	C₂²×C₁₃	C₂×C₄×C₈	1	6	yes	—
88	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
89	C₄×C₁₃	—	2	6	no	—
90	C₄×C₁₃	C₂×C₄×C₈	1	6	yes	—
91	C₄×C₁₃	C₂³×C₈	1	2	yes	—
92	C₄×C₁₃	#568	1	4	yes	—
93	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
94	#131	C₈×C₁₃	1	16	yes	complemented
95	C₂×M₁₆	C₂×C₄×C₁₃	1	6	yes	—
96	C₂²×C₈	C₂×C₄×C₁₃	1	12	yes	—
97	C₂²×C₈	C₂×C₄×C₁₃	1	6	yes	—
98	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
99	C₄×D₄	C₂×C₄×C₁₃	1	6	yes	—
100	#117	C₂×C₄×C₁₃	1	3	yes	—
101	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
102	C₄⋊C₈	C₂×C₄×C₁₃	1	12	yes	—
103	C₂²⋊C₈	C₂×C₄×C₁₃	1	12	yes	—
104	#97	C₂×C₄×C₁₃	1	6	yes	—
105	C₄×C₈	C₂×C₄×C₁₃	1	6	yes	—
106	C₄×C₈	C₂×C₄×C₁₃	1	12	yes	—
107	C₄×C₈	C₂³×C₁₃	1	3	yes	—
108	C₄×C₈	C₂³×C₁₃	1	6	yes	—
109	C₄×C₈	C₂³×C₁₃	1	2	yes	—
110	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
111	C₂×C₁₃	—	2	6	no	—
112	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
113	C₂×C₁₃	#2875	1	2	yes	—
114	#41	C₂×C₈×C₁₃	1	8	yes	—
115	C₂×Q₈	C₄²×C₁₃	1	1	yes	characteristic
116	C₂×D₄	C₄²×C₁₃	1	3	yes	—
117	C₂²×C₄	C₂²×C₄×C₁₃	1	6	yes	—
118	C₂²×C₄	C₂²×C₄×C₁₃	1	3	yes	—
119	M₁₆	C₂×C₈×C₁₃	1	24	yes	complemented
120	C₂×C₈	—	4	12	no	—
121	C₂×C₈	C₂×C₈×C₁₃	1	24	yes	complemented
122	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
123	C₂×C₈	C₂²×C₄×C₁₃	1	12	yes	—
124	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
125	C₂×C₈	C₂²×C₄×C₁₃	1	6	yes	—
126	C₄⋊C₄	C₄²×C₁₃	1	6	yes	—
127	C₂²⋊C₄	C₄²×C₁₃	1	6	yes	—
128	C₄²	C₂²×C₄×C₁₃	1	3	yes	—
129	C₄²	C₂²×C₄×C₁₃	1	6	yes	—
130	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
131	C₁₃	#17316	1	1	yes	characteristic, direct product factor, Sylow
132	C₂³	C₂×C₄²×C₁₃	1	3	yes	—
133	Q₈	C₄×C₈×C₁₃	1	4	yes	—
134	D₄	C₄×C₈×C₁₃	1	12	yes	—
135	C₂×C₄	—	2	12	no	—
136	C₂×C₄	C₂×C₄²×C₁₃	1	6	yes	—
137	C₂×C₄	C₂×C₄²×C₁₃	1	3	yes	—
138	C₂×C₄	C₂²×C₈×C₁₃	1	12	yes	—
139	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
140	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
141	C₈	—	2	4	no	—
142	C₈	—	2	12	no	—
143	C₈	C₂²×C₈×C₁₃	1	4	yes	—
144	C₈	C₂²×C₈×C₁₃	1	12	yes	—
145	C₂²	—	2	6	no	—
146	C₂²	C₂×C₄×C₈×C₁₃	1	6	yes	—
147	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
148	C₄	—	2	6	no	—
149	C₄	C₂×C₄×C₈×C₁₃	1	6	yes	—
150	C₄	C₂³×C₈×C₁₃	1	2	yes	—
151	C₄	C₁₃×#568	1	4	yes	—
152	C₂	—	2	6	no	—
153	C₂	C₂²×C₄×C₈×C₁₃	1	1	yes	characteristic
154	C₂	C₁₃×#2875	1	2	yes	—

	subgroup	G/H
center	C₄²×C₁₃	C₂⁴
commutator	C₂	C₂²×C₄×C₈×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂²×C₄²
prime radical	C₂×C₁₃×#41	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#1450	C₂	semidirect
4. C₈×C₁₃×M₁₆	C₂	semidirect
5. C₂×C₁₃×#322	C₂	semidirect
20. C₁₃×#131	C₈	semidirect
37. #17316	C₁₃	direct (N × H)
43. C₁₃×M₁₆	C₂×C₈	semidirect
45. C₂×C₈×C₁₃	C₂×C₈	semidirect
57. #1450	C₂×C₁₃	semidirect
58. C₈×M₁₆	C₂×C₁₃	semidirect
59. C₂×#322	C₂×C₁₃	semidirect
94. #131	C₈×C₁₃	semidirect
119. M₁₆	C₂×C₈×C₁₃	semidirect
121. C₂×C₈	C₂×C₈×C₁₃	semidirect
131. C₁₃	#17316	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×C₁₃×#41	2
C₄×C₁₃×#131	2
C₁₃×#1450	2
C₈×C₁₃×M₁₆	2
C₂×C₁₃×#322	2
#17316	13

Subgroups — C13×#17316 #15703655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17316 #15703655