Subgroups — C₁₃×#12887 #15699226

Order 3328.

286 conjugacy classes of subgroups.

The subgroup lattice has 172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1848	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1846	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1383	C₂	1	4	yes	maximal
5	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
6	C₂×C₁₃×#108	—	2	1	no	—
7	C₂×C₁₃×#108	C₂²	1	2	yes	—
8	C₂×C₁₃×#107	—	2	1	no	—
9	C₂×C₁₃×#106	C₂²	1	2	yes	—
10	C₁₃×#423	—	2	1	no	—
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#382	—	2	1	no	—
13	C₁₃×#346	C₄	1	2	yes	complemented
14	C₄×C₁₃×C₁₆	C₄	1	2	yes	complemented
15	C₂×C₁₃×M₁₆	—	2	2	no	—
16	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
19	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
20	C₁₃×M₃₂	—	2	2	no	—
21	C₁₃×M₃₂	—	2	2	no	—
22	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
23	C₁₃×#108	—	2	4	no	—
24	C₁₃×#108	—	4	2	no	—
25	C₁₃×#107	—	4	2	no	—
26	C₁₃×#106	—	2	4	no	—
27	C₁₃×C₄⋊C₈	—	4	2	no	—
28	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
31	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
32	C₁₃×#95	—	4	2	no	—
33	#12887	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₂²×C₄×C₁₃	—	4	2	no	—
35	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
36	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
37	C₁₃×M₁₆	—	4	2	no	—
38	C₁₃×M₁₆	—	4	2	no	—
39	C₂×C₈×C₁₃	—	4	2	no	—
40	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₃	D₈	1	2	yes	—
43	C₂×C₈×C₁₃	Q₁₆	1	2	yes	—
44	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₈×C₁₃	#41	1	2	yes	—
47	C₂×C₈×C₁₃	#41	1	2	yes	—
48	C₁₃×C₄⋊C₄	—	4	2	no	—
49	C₁₃×C₄⋊C₄	—	4	2	no	—
50	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
51	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
52	C₄²×C₁₃	SD₁₆	1	2	yes	—
53	C₁₃×C₁₆	—	2	4	no	—
54	C₄×M₃₂	C₂×C₁₃	1	1	yes	characteristic
55	#1848	C₂×C₁₃	1	1	yes	characteristic
56	#1846	C₂×C₁₃	1	1	yes	characteristic
57	#1383	C₂×C₁₃	1	4	yes	—
58	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
59	C₂×C₄×C₁₃	—	4	2	no	—
60	C₂×C₄×C₁₃	—	8	4	no	—
61	C₂×C₄×C₁₃	—	8	2	no	—
62	C₂×C₄×C₁₃	#106	1	2	yes	—
63	C₂×C₄×C₁₃	#106	1	2	yes	—
64	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
66	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
67	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
68	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
69	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
70	C₈×C₁₃	—	8	2	no	—
71	C₈×C₁₃	#107	1	2	yes	—
72	C₈×C₁₃	#107	1	2	yes	—
73	C₈×C₁₃	#117	1	2	yes	—
74	C₈×C₁₃	#125	1	2	yes	—
75	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
76	C₂×#108	—	2	1	no	—
77	C₂×#108	C₂²×C₁₃	1	2	yes	—
78	C₂×#107	—	2	1	no	—
79	C₂×#106	C₂²×C₁₃	1	2	yes	—
80	#423	—	2	1	no	—
81	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
82	#382	—	2	1	no	—
83	#346	C₄×C₁₃	1	2	yes	complemented
84	C₄×C₁₆	C₄×C₁₃	1	2	yes	complemented
85	C₂²×C₁₃	—	2	2	no	—
86	C₂²×C₁₃	C₂×#106	1	1	yes	characteristic
87	C₂²×C₁₃	#486	1	1	yes	characteristic
88	C₂²×C₁₃	#487	1	1	yes	characteristic
89	C₄×C₁₃	—	2	2	no	—
90	C₄×C₁₃	—	2	2	no	—
91	C₄×C₁₃	—	16	2	no	—
92	C₄×C₁₃	#382	1	1	yes	characteristic
93	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
94	C₄×C₁₃	#486	1	1	yes	characteristic
95	C₄×C₁₃	#487	1	1	yes	characteristic
96	C₂×M₁₆	—	2	2	no	—
97	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
98	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
99	C₂×C₄⋊C₄	—	2	2	no	—
100	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
101	M₃₂	—	2	2	no	—
102	M₃₂	—	2	2	no	—
103	C₂×C₁₆	C₂×C₄×C₁₃	1	4	yes	—
104	#108	—	2	4	no	—
105	#108	—	4	2	no	—
106	#107	—	4	2	no	—
107	#106	—	2	4	no	—
108	C₄⋊C₈	—	4	2	no	—
109	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
110	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
111	C₄×C₈	Q₈×C₁₃	1	1	yes	characteristic
112	C₄×C₈	Q₈×C₁₃	1	1	yes	characteristic
113	#95	—	4	2	no	—
114	C₂×C₁₃	—	2	1	no	—
115	C₂×C₁₃	—	2	1	no	—
116	C₂×C₁₃	#1834	1	1	yes	characteristic
117	C₂×C₁₃	#2155	1	2	yes	—
118	C₂²×C₄	—	4	2	no	—
119	C₂²×C₄	C₁₃×SD₁₆	1	2	yes	—
120	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
121	M₁₆	—	4	2	no	—
122	M₁₆	—	4	2	no	—
123	C₂×C₈	—	4	2	no	—
124	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₈	C₁₃×D₈	1	2	yes	—
127	C₂×C₈	C₁₃×Q₁₆	1	2	yes	—
128	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
129	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
130	C₂×C₈	C₁₃×#41	1	2	yes	—
131	C₂×C₈	C₁₃×#41	1	2	yes	—
132	C₄⋊C₄	—	4	2	no	—
133	C₄⋊C₄	—	4	2	no	—
134	C₄²	C₁₃×C₄⋊C₄	1	1	yes	characteristic
135	C₄²	C₁₃×C₄⋊C₄	1	1	yes	characteristic
136	C₄²	C₁₃×SD₁₆	1	2	yes	—
137	C₁₆	—	2	4	no	—
138	C₁₃	#12887	1	1	yes	characteristic, direct product factor, Sylow
139	C₂³	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
140	C₂×C₄	—	4	2	no	—
141	C₂×C₄	—	8	4	no	—
142	C₂×C₄	—	8	2	no	—
143	C₂×C₄	C₁₃×#106	1	2	yes	—
144	C₂×C₄	C₁₃×#106	1	2	yes	—
145	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
147	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
148	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
149	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
150	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
151	C₈	—	8	2	no	—
152	C₈	C₁₃×#107	1	2	yes	—
153	C₈	C₁₃×#107	1	2	yes	—
154	C₈	C₁₃×#117	1	2	yes	—
155	C₈	C₁₃×#125	1	2	yes	—
156	C₂²	—	2	2	no	—
157	C₂²	C₂×C₁₃×#106	1	1	yes	characteristic
158	C₂²	C₁₃×#486	1	1	yes	characteristic
159	C₂²	C₁₃×#487	1	1	yes	characteristic
160	C₄	—	2	2	no	—
161	C₄	—	2	2	no	—
162	C₄	—	16	2	no	—
163	C₄	C₁₃×#382	1	1	yes	characteristic
164	C₄	C₂×C₁₃×#107	1	1	yes	characteristic
165	C₄	C₁₃×#486	1	1	yes	characteristic
166	C₄	C₁₃×#487	1	1	yes	characteristic
167	C₂	—	2	1	no	—
168	C₂	—	2	1	no	—
169	C₂	C₁₃×#1834	1	1	yes	characteristic
170	C₂	C₁₃×#2155	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#106
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	C₂×SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₁₃×#346	C₄	semidirect
14. C₄×C₁₃×C₁₆	C₄	semidirect
33. #12887	C₁₃	direct (N × H)
83. #346	C₄×C₁₃	semidirect
84. C₄×C₁₆	C₄×C₁₃	semidirect
138. C₁₃	#12887	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×M₃₂	2
C₁₃×#1848	2
C₁₃×#1846	2
C₁₃×#1383	2
#12887	13

Subgroups — C13×#12887 #15699226

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12887 #15699226