Subgroups — C₁₃×#20507 #15706846

Order 3328.

1054 conjugacy classes of subgroups.

The subgroup lattice has 166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×Q₁₆	C₂	1	3	yes	maximal
2	C₁₃×#2276	C₂	1	2	yes	maximal
3	C₄×C₁₃×#107	C₂	1	3	yes	maximal
4	C₁₃×#1763	C₂	1	6	yes	maximal
5	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₁₃	C₂²	1	6	yes	—
8	C₄×C₁₃×Q₁₆	C₄	1	24	yes	complemented
9	C₂×C₁₃×#107	C₂²	1	3	yes	—
10	C₂×C₁₃×#103	C₂²	1	6	yes	—
11	C₂×C₁₃×#97	C₂²	1	3	yes	—
12	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
13	C₄×C₁₃×C₄⋊C₄	—	2	6	no	—
14	C₄×C₁₃×C₄⋊C₄	C₂²	1	6	yes	—
15	C₁₃×#376	—	2	2	no	—
16	C₁₃×#376	C₂²	1	1	yes	characteristic
17	C₁₃×#340	C₂²	1	6	yes	—
18	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
19	C₂×C₁₃×Q₁₆	C₂×C₄	1	12	yes	—
20	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
21	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
22	C₄×Q₈×C₁₃	—	2	12	no	—
23	C₄×Q₈×C₁₃	C₂×C₄	1	24	yes	—
24	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
25	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
26	C₂×C₄²×C₁₃	—	2	6	no	—
27	C₂×C₄²×C₁₃	—	2	6	no	—
28	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
29	C₁₃×#107	C₂×C₄	1	12	yes	—
30	C₁₃×#103	C₂×C₄	1	24	yes	—
31	C₁₃×#97	—	2	6	no	—
32	C₄×C₈×C₁₃	C₂×C₄	1	12	yes	—
33	C₁₃×#95	—	2	6	no	—
34	C₁₃×#95	D₄	1	3	yes	—
35	C₁₃×#95	D₄	1	1	yes	characteristic
36	#20507	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂×Q₈×C₁₃	—	2	6	no	—
38	C₂×Q₈×C₁₃	C₂²×C₄	1	12	yes	—
39	C₂²×C₄×C₁₃	—	2	2	no	—
40	C₂²×C₄×C₁₃	—	2	6	no	—
41	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
42	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
43	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
44	C₁₃×Q₁₆	C₄²	1	16	yes	complemented
45	C₂×C₈×C₁₃	—	2	6	no	—
46	C₂×C₈×C₁₃	C₂²×C₄	1	6	yes	—
47	C₂×C₈×C₁₃	C₂²×C₄	1	6	yes	—
48	C₁₃×C₄⋊C₄	—	2	24	no	—
49	C₁₃×C₄⋊C₄	—	2	6	no	—
50	C₁₃×C₄⋊C₄	C₂²×C₄	1	12	yes	—
51	C₄²×C₁₃	—	2	24	no	—
52	C₄²×C₁₃	—	8	6	no	—
53	C₄²×C₁₃	C₂²×C₄	1	6	yes	—
54	C₄²×C₁₃	#41	1	6	yes	—
55	C₂×C₄×Q₁₆	C₂×C₁₃	1	3	yes	—
56	#2276	C₂×C₁₃	1	2	yes	—
57	C₄×#107	C₂×C₁₃	1	3	yes	—
58	#1763	C₂×C₁₃	1	6	yes	—
59	#1726	C₂×C₁₃	1	1	yes	characteristic
60	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
61	Q₈×C₁₃	—	2	12	no	—
62	Q₈×C₁₃	C₂×C₄²	1	8	yes	—
63	C₂×C₄×C₁₃	—	2	12	no	—
64	C₂×C₄×C₁₃	—	2	3	no	—
65	C₂×C₄×C₁₃	—	2	6	no	—
66	C₂×C₄×C₁₃	—	2	3	no	—
67	C₂×C₄×C₁₃	—	2	12	no	—
68	C₂×C₄×C₁₃	—	4	6	no	—
69	C₂×C₄×C₁₃	—	4	6	no	—
70	C₂×C₄×C₁₃	C₄×D₄	1	6	yes	—
71	C₂×C₄×C₁₃	C₄×D₄	1	6	yes	—
72	C₂×C₄×C₁₃	C₂³×C₄	1	3	yes	—
73	C₂×C₄×C₁₃	C₂×#41	1	3	yes	—
74	C₈×C₁₃	—	2	6	no	—
75	C₈×C₁₃	C₂×C₄²	1	4	yes	—
76	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
77	C₂×C₄×Q₈	C₂²×C₁₃	1	6	yes	—
78	C₄×Q₁₆	C₄×C₁₃	1	24	yes	complemented
79	C₂×#107	C₂²×C₁₃	1	3	yes	—
80	C₂×#103	C₂²×C₁₃	1	6	yes	—
81	C₂×#97	C₂²×C₁₃	1	3	yes	—
82	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	—
83	C₄×C₄⋊C₄	—	2	6	no	—
84	C₄×C₄⋊C₄	C₂²×C₁₃	1	6	yes	—
85	#376	—	2	2	no	—
86	#376	C₂²×C₁₃	1	1	yes	characteristic
87	#340	C₂²×C₁₃	1	6	yes	—
88	C₂²×C₁₃	C₂×C₄×D₄	1	3	yes	—
89	C₂²×C₁₃	#576	1	1	yes	characteristic
90	C₂²×C₁₃	#578	1	3	yes	—
91	C₄×C₁₃	—	2	6	no	—
92	C₄×C₁₃	—	2	6	no	—
93	C₄×C₁₃	—	2	8	no	—
94	C₄×C₁₃	—	4	12	no	—
95	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
96	C₄×C₁₃	C₄×#41	1	3	yes	—
97	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
98	C₂×Q₁₆	C₂×C₄×C₁₃	1	12	yes	—
99	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
100	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
101	C₄×Q₈	—	2	12	no	—
102	C₄×Q₈	C₂×C₄×C₁₃	1	24	yes	—
103	C₂×C₄⋊C₄	—	2	6	no	—
104	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
105	C₂×C₄²	—	2	6	no	—
106	C₂×C₄²	—	2	6	no	—
107	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
108	#107	C₂×C₄×C₁₃	1	12	yes	—
109	#103	C₂×C₄×C₁₃	1	24	yes	—
110	#97	—	2	6	no	—
111	C₄×C₈	C₂×C₄×C₁₃	1	12	yes	—
112	#95	—	2	6	no	—
113	#95	D₄×C₁₃	1	1	yes	characteristic
114	#95	D₄×C₁₃	1	3	yes	—
115	C₂×C₁₃	C₄²×D₄	1	1	yes	characteristic
116	C₂×C₁₃	#2950	1	3	yes	—
117	C₂×C₁₃	#2951	1	3	yes	—
118	C₂×Q₈	—	2	6	no	—
119	C₂×Q₈	C₂²×C₄×C₁₃	1	12	yes	—
120	C₂²×C₄	—	2	2	no	—
121	C₂²×C₄	—	2	6	no	—
122	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
123	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
124	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
125	Q₁₆	C₄²×C₁₃	1	16	yes	complemented
126	C₂×C₈	—	2	6	no	—
127	C₂×C₈	C₂²×C₄×C₁₃	1	6	yes	—
128	C₂×C₈	C₂²×C₄×C₁₃	1	6	yes	—
129	C₄⋊C₄	—	2	24	no	—
130	C₄⋊C₄	—	2	6	no	—
131	C₄⋊C₄	C₂²×C₄×C₁₃	1	12	yes	—
132	C₄²	—	2	24	no	—
133	C₄²	—	8	6	no	—
134	C₄²	C₂²×C₄×C₁₃	1	6	yes	—
135	C₄²	C₁₃×#41	1	6	yes	—
136	C₁₃	#20507	1	1	yes	characteristic, direct product factor, Sylow
137	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
138	Q₈	—	2	12	no	—
139	Q₈	C₂×C₄²×C₁₃	1	8	yes	—
140	C₂×C₄	—	2	12	no	—
141	C₂×C₄	—	2	3	no	—
142	C₂×C₄	—	2	6	no	—
143	C₂×C₄	—	2	3	no	—
144	C₂×C₄	—	2	12	no	—
145	C₂×C₄	—	4	6	no	—
146	C₂×C₄	—	4	6	no	—
147	C₂×C₄	C₄×D₄×C₁₃	1	6	yes	—
148	C₂×C₄	C₄×D₄×C₁₃	1	6	yes	—
149	C₂×C₄	C₂³×C₄×C₁₃	1	3	yes	—
150	C₂×C₄	C₂×C₁₃×#41	1	3	yes	—
151	C₈	—	2	6	no	—
152	C₈	C₂×C₄²×C₁₃	1	4	yes	—
153	C₂²	C₂×C₄×D₄×C₁₃	1	3	yes	—
154	C₂²	C₁₃×#576	1	1	yes	characteristic
155	C₂²	C₁₃×#578	1	3	yes	—
156	C₄	—	2	8	no	—
157	C₄	—	2	6	no	—
158	C₄	—	2	6	no	—
159	C₄	—	4	12	no	—
160	C₄	C₂²×C₄²×C₁₃	1	1	yes	characteristic
161	C₄	C₄×C₁₃×#41	1	3	yes	—
162	C₂	C₄²×D₄×C₁₃	1	1	yes	characteristic
163	C₂	C₁₃×#2950	1	3	yes	—
164	C₂	C₁₃×#2951	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂²×D₄
commutator	C₄	C₂²×C₄²×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₁₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
8. C₄×C₁₃×Q₁₆	C₄	semidirect
36. #20507	C₁₃	direct (N × H)
44. C₁₃×Q₁₆	C₄²	semidirect
78. C₄×Q₁₆	C₄×C₁₃	semidirect
125. Q₁₆	C₄²×C₁₃	semidirect
136. C₁₃	#20507	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₁₃×Q₁₆	2
C₁₃×#2276	2
C₄×C₁₃×#107	2
C₁₃×#1763	2
C₁₃×#1726	2
#20507	13

Subgroups — C13×#20507 #15706846

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20507 #15706846