Subgroups — C₁₃×#12656 #15698995

Order 3328.

358 conjugacy classes of subgroups.

The subgroup lattice has 184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#364	C₂	1	2	yes	maximal
2	C₄×C₁₃×M₃₂	C₂	1	2	yes	maximal
3	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1376	C₂	1	2	yes	maximal
5	C₂×C₁₃×M₃₂	C₂²	1	4	yes	—
6	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
7	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
8	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
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	C₁₃×#376	C₄	1	1	yes	characteristic
13	C₁₃×#364	C₄	1	8	yes	complemented
14	C₁₃×#346	—	2	2	no	—
15	C₄×C₁₃×C₁₆	—	2	2	no	—
16	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
20	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₁₃×M₃₂	—	2	4	no	—
24	C₁₃×M₃₂	C₂×C₄	1	8	yes	—
25	C₂×C₁₃×C₁₆	—	2	4	no	—
26	C₁₃×#97	—	2	2	no	—
27	C₁₃×#97	C₈	1	4	yes	—
28	C₁₃×#97	C₈	1	4	yes	—
29	C₄×C₈×C₁₃	—	2	2	no	—
30	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
31	C₄×C₈×C₁₃	D₄	1	2	yes	—
32	C₄×C₈×C₁₃	Q₈	1	2	yes	—
33	C₁₃×#95	—	2	2	no	—
34	#12656	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂²×C₄×C₁₃	—	2	1	no	—
36	C₂²×C₄×C₁₃	—	2	1	no	—
37	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
38	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₃	—	2	1	no	—
40	C₂×C₈×C₁₃	—	2	1	no	—
41	C₂×C₈×C₁₃	C₄²	1	2	yes	—
42	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
43	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
44	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
45	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
46	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
47	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
48	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
49	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
50	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₈×C₁₃	#41	1	2	yes	—
52	C₄²×C₁₃	—	2	1	no	—
53	C₄²×C₁₃	—	2	1	no	—
54	C₄²×C₁₃	C₄²	1	2	yes	—
55	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
56	C₄²×C₁₃	C₂×C₈	1	2	yes	—
57	C₄²×C₁₃	C₂×C₈	1	2	yes	—
58	C₁₃×C₁₆	—	2	8	no	—
59	C₂×#364	C₂×C₁₃	1	2	yes	—
60	C₄×M₃₂	C₂×C₁₃	1	2	yes	—
61	#1726	C₂×C₁₃	1	1	yes	characteristic
62	#1376	C₂×C₁₃	1	2	yes	—
63	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
64	C₂×C₄×C₁₃	—	2	2	no	—
65	C₂×C₄×C₁₃	—	2	2	no	—
66	C₂×C₄×C₁₃	—	4	2	no	—
67	C₂×C₄×C₁₃	—	4	2	no	—
68	C₂×C₄×C₁₃	—	4	2	no	—
69	C₂×C₄×C₁₃	C₄⋊C₈	1	4	yes	—
70	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
71	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
72	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
73	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
74	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
75	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
76	C₈×C₁₃	—	2	2	no	—
77	C₈×C₁₃	C₄×C₈	1	4	yes	—
78	C₈×C₁₃	C₄⋊C₈	1	4	yes	—
79	C₈×C₁₃	C₄×D₄	1	2	yes	—
80	C₈×C₁₃	C₄×Q₈	1	2	yes	—
81	C₂×M₃₂	C₂²×C₁₃	1	4	yes	—
82	C₂×#97	C₄×C₁₃	1	1	yes	characteristic
83	C₂×#97	C₄×C₁₃	1	1	yes	characteristic
84	C₂×#97	C₄×C₁₃	1	1	yes	characteristic
85	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
86	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
87	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
88	#376	C₄×C₁₃	1	1	yes	characteristic
89	#364	C₄×C₁₃	1	8	yes	complemented
90	#346	—	2	2	no	—
91	C₄×C₁₆	—	2	2	no	—
92	C₂²×C₁₃	—	2	2	no	—
93	C₂²×C₁₃	C₄×M₁₆	1	1	yes	characteristic
94	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
95	C₂²×C₁₃	#431	1	1	yes	characteristic
96	C₄×C₁₃	—	2	4	no	—
97	C₄×C₁₃	—	4	2	no	—
98	C₄×C₁₃	—	4	2	no	—
99	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
100	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
101	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
102	C₄×C₁₃	#431	1	1	yes	characteristic
103	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
104	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
105	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
106	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
107	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
108	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
109	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
110	M₃₂	—	2	4	no	—
111	M₃₂	C₂×C₄×C₁₃	1	8	yes	—
112	C₂×C₁₆	—	2	4	no	—
113	#97	—	2	2	no	—
114	#97	C₈×C₁₃	1	4	yes	—
115	#97	C₈×C₁₃	1	4	yes	—
116	C₄×C₈	—	2	2	no	—
117	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
118	C₄×C₈	D₄×C₁₃	1	2	yes	—
119	C₄×C₈	Q₈×C₁₃	1	2	yes	—
120	#95	—	2	2	no	—
121	C₂×C₁₃	—	2	1	no	—
122	C₂×C₁₃	—	2	1	no	—
123	C₂×C₁₃	C₄×C₄⋊C₈	1	1	yes	characteristic
124	C₂×C₁₃	#2153	1	2	yes	—
125	C₂²×C₄	—	2	1	no	—
126	C₂²×C₄	—	2	1	no	—
127	C₂²×C₄	C₁₃×M₁₆	1	2	yes	—
128	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
129	C₂×C₈	—	2	1	no	—
130	C₂×C₈	—	2	1	no	—
131	C₂×C₈	C₄²×C₁₃	1	2	yes	—
132	C₂×C₈	C₁₃×C₄⋊C₄	1	2	yes	—
133	C₂×C₈	C₂×C₈×C₁₃	1	2	yes	—
134	C₂×C₈	C₂×C₈×C₁₃	1	2	yes	—
135	C₂×C₈	C₂×C₈×C₁₃	1	2	yes	—
136	C₂×C₈	C₂×C₈×C₁₃	1	2	yes	—
137	C₂×C₈	C₁₃×M₁₆	1	2	yes	—
138	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
139	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
140	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
141	C₂×C₈	C₁₃×#41	1	2	yes	—
142	C₄²	—	2	1	no	—
143	C₄²	—	2	1	no	—
144	C₄²	C₄²×C₁₃	1	2	yes	—
145	C₄²	C₁₃×C₄⋊C₄	1	2	yes	—
146	C₄²	C₂×C₈×C₁₃	1	2	yes	—
147	C₄²	C₂×C₈×C₁₃	1	2	yes	—
148	C₁₆	—	2	8	no	—
149	C₁₃	#12656	1	1	yes	characteristic, direct product factor, Sylow
150	C₂³	C₂×C₁₃×M₁₆	1	1	yes	characteristic
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	4	2	no	—
154	C₂×C₄	—	4	2	no	—
155	C₂×C₄	—	4	2	no	—
156	C₂×C₄	C₁₃×C₄⋊C₈	1	4	yes	—
157	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
158	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄	C₁₃×#117	1	1	yes	characteristic
160	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
161	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
162	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
163	C₈	—	2	2	no	—
164	C₈	C₄×C₈×C₁₃	1	4	yes	—
165	C₈	C₁₃×C₄⋊C₈	1	4	yes	—
166	C₈	C₄×D₄×C₁₃	1	2	yes	—
167	C₈	C₄×Q₈×C₁₃	1	2	yes	—
168	C₂²	—	2	2	no	—
169	C₂²	C₄×C₁₃×M₁₆	1	1	yes	characteristic
170	C₂²	C₂×C₁₃×C₄⋊C₈	1	1	yes	characteristic
171	C₂²	C₁₃×#431	1	1	yes	characteristic
172	C₄	—	2	4	no	—
173	C₄	—	4	2	no	—
174	C₄	—	4	2	no	—
175	C₄	C₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
176	C₄	C₂×C₄×C₈×C₁₃	1	1	yes	characteristic
177	C₄	C₂×C₁₃×C₄⋊C₈	1	1	yes	characteristic
178	C₄	C₁₃×#431	1	1	yes	characteristic
179	C₂	—	2	1	no	—
180	C₂	—	2	1	no	—
181	C₂	C₄×C₁₃×C₄⋊C₈	1	1	yes	characteristic
182	C₂	C₁₃×#2153	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₁₃	C₂×D₄
commutator	C₄	C₂×C₄×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×C₄⋊C₈
prime radical	C₂³×C₁₃	C₂×M₁₆
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₁₃×#364	C₄	semidirect
34. #12656	C₁₃	direct (N × H)
89. #364	C₄×C₁₃	semidirect
149. C₁₃	#12656	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×C₁₃×#364	2
C₄×C₁₃×M₃₂	2
C₁₃×#1726	2
C₁₃×#1376	2
#12656	13

Subgroups — C13×#12656 #15698995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12656 #15698995