Subgroups — C₁₃×#3352 #13112410

Order 1664.

336 conjugacy classes of subgroups.

The subgroup lattice has 194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#552	C₂	1	2	yes	maximal
2	C₁₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#485	C₂	1	2	yes	maximal, complemented
4	C₁₃×#484	C₂	1	2	yes	maximal, complemented
5	C₁₃×#479	C₂	1	2	yes	maximal, complemented
6	C₁₃×#470	C₂	1	2	yes	maximal, complemented
7	C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#436	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#428	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
12	C₁₃×#126	—	2	2	no	—
13	C₁₃×#125	—	2	2	no	—
14	C₁₃×#125	C₂²	1	2	yes	—
15	C₁₃×#123	—	2	2	no	—
16	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
17	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
19	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#117	—	2	2	no	—
21	C₁₃×#117	C₂²	1	2	yes	—
22	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
23	C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₁₃×#107	C₂²	1	2	yes	—
25	C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₁₃×#107	C₂²	1	1	yes	characteristic
27	C₁₃×#106	C₂²	1	2	yes	—
28	C₁₃×#106	C₂²	1	2	yes	—
29	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₁₃×#103	C₂²	1	2	yes	—
31	C₁₃×#103	C₂²	1	2	yes	—
32	C₁₃×#103	C₂²	1	2	yes	—
33	C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
34	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
36	C₂×D₄×C₁₃	D₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₃	—	2	2	no	—
38	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
39	C₁₃×Q₁₆	—	2	2	no	—
40	C₁₃×M₁₆	—	2	4	no	—
41	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
42	C₂×C₈×C₁₃	C₂³	1	2	yes	—
43	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₁₃×C₄⋊C₄	—	2	2	no	—
45	C₁₃×C₄⋊C₄	—	2	2	no	—
46	C₁₃×C₄⋊C₄	—	2	2	no	—
47	C₁₃×C₄⋊C₄	—	2	2	no	—
48	C₁₃×C₄⋊C₄	—	2	2	no	—
49	C₁₃×C₄⋊C₄	—	2	2	no	—
50	C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
51	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
52	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
53	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
54	C₁₃×C₂²⋊C₄	—	2	2	no	—
55	C₁₃×C₂²⋊C₄	—	2	2	no	—
56	C₁₃×C₂²⋊C₄	—	2	2	no	—
57	C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
58	C₄²×C₁₃	—	2	2	no	—
59	C₄²×C₁₃	—	2	2	no	—
60	C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	#3352	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂³×C₁₃	C₂×D₄	1	2	yes	—
63	Q₈×C₁₃	—	2	2	no	—
64	Q₈×C₁₃	—	2	2	no	—
65	D₄×C₁₃	—	4	1	no	—
66	C₂×C₄×C₁₃	—	2	2	no	—
67	C₂×C₄×C₁₃	—	2	2	no	—
68	C₂×C₄×C₁₃	—	2	2	no	—
69	C₂×C₄×C₁₃	—	2	2	no	—
70	C₂×C₄×C₁₃	—	2	2	no	—
71	C₂×C₄×C₁₃	—	2	2	no	—
72	C₂×C₄×C₁₃	—	4	4	no	—
73	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
74	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
75	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
76	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
77	C₈×C₁₃	—	2	2	no	—
78	C₈×C₁₃	—	2	1	no	—
79	C₈×C₁₃	#41	1	2	yes	—
80	#552	C₂×C₁₃	1	2	yes	—
81	#499	C₂×C₁₃	1	1	yes	characteristic, complemented
82	#485	C₂×C₁₃	1	2	yes	complemented
83	#484	C₂×C₁₃	1	2	yes	complemented
84	#479	C₂×C₁₃	1	2	yes	complemented
85	#470	C₂×C₁₃	1	2	yes	complemented
86	C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
87	#436	C₂×C₁₃	1	1	yes	characteristic
88	#428	C₂×C₁₃	1	2	yes	complemented
89	C₂²×C₁₃	—	2	2	no	—
90	C₂²×C₁₃	—	2	2	no	—
91	C₂²×C₁₃	—	2	2	no	—
92	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
93	C₄×C₁₃	—	2	2	no	—
94	C₄×C₁₃	—	2	1	no	—
95	C₄×C₁₃	—	2	1	no	—
96	C₄×C₁₃	—	4	2	no	—
97	C₄×C₁₃	—	4	2	no	—
98	C₄×C₁₃	—	4	2	no	—
99	C₄×C₁₃	—	4	2	no	—
100	C₄×C₁₃	C₂×#41	1	1	yes	characteristic
101	C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
102	C₂×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
103	C₂×M₁₆	C₂²×C₁₃	1	2	yes	—
104	#126	—	2	2	no	—
105	#125	—	2	2	no	—
106	#125	C₂²×C₁₃	1	2	yes	—
107	#123	—	2	2	no	—
108	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
109	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
110	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
111	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
112	#117	—	2	2	no	—
113	#117	C₂²×C₁₃	1	2	yes	—
114	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
115	#107	C₂²×C₁₃	1	1	yes	characteristic
116	#107	C₂²×C₁₃	1	2	yes	—
117	#107	C₂²×C₁₃	1	1	yes	characteristic
118	#107	C₂²×C₁₃	1	1	yes	characteristic
119	#106	C₂²×C₁₃	1	2	yes	—
120	#106	C₂²×C₁₃	1	2	yes	—
121	C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
122	#103	C₂²×C₁₃	1	2	yes	—
123	#103	C₂²×C₁₃	1	2	yes	—
124	#103	C₂²×C₁₃	1	2	yes	—
125	C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
126	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
127	C₂×C₁₃	—	4	2	no	—
128	C₂×C₁₃	#547	1	1	yes	characteristic
129	C₂×C₁₃	#575	1	1	yes	characteristic
130	C₂×C₁₃	#578	1	1	yes	characteristic
131	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
132	C₂×D₄	D₄×C₁₃	1	1	yes	characteristic
133	C₂²×C₄	—	2	2	no	—
134	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
135	Q₁₆	—	2	2	no	—
136	M₁₆	—	2	4	no	—
137	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
138	C₂×C₈	C₂³×C₁₃	1	2	yes	—
139	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
140	C₄⋊C₄	—	2	2	no	—
141	C₄⋊C₄	—	2	2	no	—
142	C₄⋊C₄	—	2	2	no	—
143	C₄⋊C₄	—	2	2	no	—
144	C₄⋊C₄	—	2	2	no	—
145	C₄⋊C₄	—	2	2	no	—
146	C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
147	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
148	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
149	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
150	C₂²⋊C₄	—	2	2	no	—
151	C₂²⋊C₄	—	2	2	no	—
152	C₂²⋊C₄	—	2	2	no	—
153	C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
154	C₄²	—	2	2	no	—
155	C₄²	—	2	2	no	—
156	C₄²	C₂³×C₁₃	1	1	yes	characteristic
157	C₁₃	#3352	1	1	yes	characteristic, direct product factor, Sylow
158	C₂³	C₂×D₄×C₁₃	1	2	yes	—
159	Q₈	—	2	2	no	—
160	Q₈	—	2	2	no	—
161	D₄	—	4	1	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	4	4	no	—
169	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
170	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
171	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
172	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
173	C₈	—	2	2	no	—
174	C₈	—	2	1	no	—
175	C₈	C₁₃×#41	1	2	yes	—
176	C₂²	—	2	2	no	—
177	C₂²	—	2	2	no	—
178	C₂²	—	2	2	no	—
179	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
180	C₄	—	2	2	no	—
181	C₄	—	2	1	no	—
182	C₄	—	2	1	no	—
183	C₄	—	4	2	no	—
184	C₄	—	4	2	no	—
185	C₄	—	4	2	no	—
186	C₄	—	4	2	no	—
187	C₄	C₂×C₁₃×#41	1	1	yes	characteristic
188	C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
189	C₂	—	4	2	no	—
190	C₂	C₁₃×#547	1	1	yes	characteristic
191	C₂	C₁₃×#575	1	1	yes	characteristic
192	C₂	C₁₃×#578	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₃×#499	C₂	semidirect
3. C₁₃×#485	C₂	semidirect
4. C₁₃×#484	C₂	semidirect
5. C₁₃×#479	C₂	semidirect
6. C₁₃×#470	C₂	semidirect
7. C₄×C₁₃×Q₁₆	C₂	semidirect
9. C₁₃×#428	C₂	semidirect
61. #3352	C₁₃	direct (N × H)
81. #499	C₂×C₁₃	semidirect
82. #485	C₂×C₁₃	semidirect
83. #484	C₂×C₁₃	semidirect
84. #479	C₂×C₁₃	semidirect
85. #470	C₂×C₁₃	semidirect
86. C₄×Q₁₆	C₂×C₁₃	semidirect
88. #428	C₂×C₁₃	semidirect
157. C₁₃	#3352	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#552	2
C₁₃×#499	2
C₁₃×#485	2
C₁₃×#484	2
C₁₃×#479	2
C₁₃×#470	2
C₄×C₁₃×Q₁₆	2
C₁₃×#436	2
C₁₃×#428	2
#3352	13

Subgroups — C13×#3352 #13112410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3352 #13112410