Subgroups — C₁₃×#13277 #15699616

Order 3328.

366 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#499	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃×#107	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1380	C₂	1	2	yes	maximal
5	C₁₃×#1380	C₂	1	2	yes	maximal
6	C₂×C₁₃×#125	—	2	1	no	—
7	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
8	C₁₃×#499	—	2	2	no	—
9	C₁₃×#499	C₄	1	4	yes	complemented
10	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#107	C₂²	1	2	yes	—
13	C₂×C₁₃×#106	—	2	1	no	—
14	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
16	C₁₃×C₄⋊C₁₆	—	2	2	no	—
17	C₁₃×#340	—	2	1	no	—
18	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
20	C₁₃×#125	—	2	4	no	—
21	C₁₃×#125	—	4	2	no	—
22	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
23	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
24	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
25	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
26	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
27	C₂×C₄²×C₁₃	—	4	1	no	—
28	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
29	C₂×C₁₃×C₁₆	—	2	2	no	—
30	C₂×C₁₃×C₁₆	—	2	4	no	—
31	C₁₃×#107	—	2	1	no	—
32	C₁₃×#107	—	2	1	no	—
33	C₁₃×#107	—	2	2	no	—
34	C₁₃×#107	C₂×C₄	1	2	yes	—
35	C₁₃×#107	C₂×C₄	1	2	yes	—
36	C₁₃×#107	Q₈	1	4	yes	—
37	C₁₃×#106	—	2	4	no	—
38	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
39	C₄×C₈×C₁₃	D₄	1	2	yes	—
40	C₁₃×#95	—	4	1	no	—
41	#13277	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₄×C₁₃	—	4	2	no	—
43	C₂²×C₄×C₁₃	—	4	1	no	—
44	C₂²×C₄×C₁₃	—	4	1	no	—
45	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
46	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
48	C₂×C₈×C₁₃	—	2	2	no	—
49	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
50	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
52	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
53	C₂×C₈×C₁₃	#41	1	2	yes	—
54	C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₁₃×C₄⋊C₄	—	2	4	no	—
57	C₁₃×C₄⋊C₄	—	4	4	no	—
58	C₁₃×C₄⋊C₄	—	4	4	no	—
59	C₁₃×C₄⋊C₄	—	4	1	no	—
60	C₁₃×C₄⋊C₄	—	4	1	no	—
61	C₁₃×C₄⋊C₄	—	4	2	no	—
62	C₄²×C₁₃	—	8	2	no	—
63	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
64	C₄²×C₁₃	SD₁₆	1	2	yes	—
65	C₁₃×C₁₆	—	4	2	no	—
66	C₂×#499	C₂×C₁₃	1	1	yes	characteristic
67	C₂×C₄⋊C₁₆	C₂×C₁₃	1	1	yes	characteristic
68	C₄×#107	C₂×C₁₃	1	1	yes	characteristic
69	#1380	C₂×C₁₃	1	2	yes	—
70	#1380	C₂×C₁₃	1	2	yes	—
71	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
72	C₂×C₄×C₁₃	—	2	2	no	—
73	C₂×C₄×C₁₃	—	2	1	no	—
74	C₂×C₄×C₁₃	—	2	1	no	—
75	C₂×C₄×C₁₃	—	4	2	no	—
76	C₂×C₄×C₁₃	—	4	2	no	—
77	C₂×C₄×C₁₃	—	4	4	no	—
78	C₂×C₄×C₁₃	—	8	2	no	—
79	C₂×C₄×C₁₃	—	8	2	no	—
80	C₂×C₄×C₁₃	—	8	2	no	—
81	C₂×C₄×C₁₃	—	8	1	no	—
82	C₂×C₄×C₁₃	—	8	1	no	—
83	C₂×C₄×C₁₃	#102	1	2	yes	—
84	C₂×C₄×C₁₃	#102	1	2	yes	—
85	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
87	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
88	C₂×C₄×C₁₃	#137	1	2	yes	—
89	C₈×C₁₃	—	2	2	no	—
90	C₈×C₁₃	C₄×Q₈	1	2	yes	—
91	C₈×C₁₃	#124	1	1	yes	characteristic
92	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
93	C₂×#125	—	2	1	no	—
94	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
95	#499	—	2	2	no	—
96	#499	C₄×C₁₃	1	4	yes	complemented
97	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
98	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
99	C₂×#107	C₂²×C₁₃	1	2	yes	—
100	C₂×#106	—	2	1	no	—
101	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
102	C₄×C₄⋊C₄	—	2	1	no	—
103	C₄⋊C₁₆	—	2	2	no	—
104	#340	—	2	1	no	—
105	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
106	C₂²×C₁₃	#474	1	2	yes	—
107	C₂²×C₁₃	#508	1	2	yes	—
108	C₂²×C₁₃	#509	1	1	yes	characteristic
109	C₂²×C₁₃	#510	1	1	yes	characteristic
110	C₄×C₁₃	—	2	2	no	—
111	C₄×C₁₃	—	2	2	no	—
112	C₄×C₁₃	—	8	2	no	—
113	C₄×C₁₃	—	8	2	no	—
114	C₄×C₁₃	—	8	4	no	—
115	C₄×C₁₃	#391	1	1	yes	characteristic
116	C₄×C₁₃	#419	1	1	yes	characteristic
117	C₄×C₁₃	#475	1	2	yes	—
118	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
119	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
120	#125	—	2	4	no	—
121	#125	—	4	2	no	—
122	C₂×C₄⋊C₄	—	2	1	no	—
123	C₂×C₄⋊C₄	—	2	1	no	—
124	C₂×C₄⋊C₄	—	2	2	no	—
125	C₂×C₄⋊C₄	—	4	1	no	—
126	C₂×C₄⋊C₄	—	4	1	no	—
127	C₂×C₄²	—	4	1	no	—
128	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
129	C₂×C₁₆	—	2	2	no	—
130	C₂×C₁₆	—	2	4	no	—
131	#107	—	2	1	no	—
132	#107	—	2	1	no	—
133	#107	—	2	2	no	—
134	#107	C₂×C₄×C₁₃	1	2	yes	—
135	#107	C₂×C₄×C₁₃	1	2	yes	—
136	#107	Q₈×C₁₃	1	4	yes	—
137	#106	—	2	4	no	—
138	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
139	C₄×C₈	D₄×C₁₃	1	2	yes	—
140	#95	—	4	1	no	—
141	C₂×C₁₃	#1988	1	1	yes	characteristic
142	C₂×C₁₃	#2138	1	1	yes	characteristic
143	C₂×C₁₃	#2139	1	1	yes	characteristic
144	C₂×C₁₃	#2228	1	2	yes	—
145	C₂×C₁₃	#2229	1	2	yes	—
146	C₂²×C₄	—	4	2	no	—
147	C₂²×C₄	—	4	1	no	—
148	C₂²×C₄	—	4	1	no	—
149	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
150	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
151	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
152	C₂×C₈	—	2	2	no	—
153	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
154	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
155	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
156	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
157	C₂×C₈	C₁₃×#41	1	2	yes	—
158	C₄⋊C₄	—	2	2	no	—
159	C₄⋊C₄	—	2	2	no	—
160	C₄⋊C₄	—	2	4	no	—
161	C₄⋊C₄	—	4	4	no	—
162	C₄⋊C₄	—	4	4	no	—
163	C₄⋊C₄	—	4	1	no	—
164	C₄⋊C₄	—	4	1	no	—
165	C₄⋊C₄	—	4	2	no	—
166	C₄²	—	8	2	no	—
167	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
168	C₄²	C₁₃×SD₁₆	1	2	yes	—
169	C₁₆	—	4	2	no	—
170	C₁₃	#13277	1	1	yes	characteristic, direct product factor, Sylow
171	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	1	no	—
174	C₂×C₄	—	2	1	no	—
175	C₂×C₄	—	4	2	no	—
176	C₂×C₄	—	4	2	no	—
177	C₂×C₄	—	4	4	no	—
178	C₂×C₄	—	8	2	no	—
179	C₂×C₄	—	8	2	no	—
180	C₂×C₄	—	8	2	no	—
181	C₂×C₄	—	8	1	no	—
182	C₂×C₄	—	8	1	no	—
183	C₂×C₄	C₁₃×#102	1	2	yes	—
184	C₂×C₄	C₁₃×#102	1	2	yes	—
185	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
186	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
187	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
188	C₂×C₄	C₁₃×#137	1	2	yes	—
189	C₈	—	2	2	no	—
190	C₈	C₄×Q₈×C₁₃	1	2	yes	—
191	C₈	C₁₃×#124	1	1	yes	characteristic
192	C₈	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
193	C₂²	C₂×C₁₃×#102	1	1	yes	characteristic
194	C₂²	C₁₃×#474	1	2	yes	—
195	C₂²	C₁₃×#508	1	2	yes	—
196	C₂²	C₁₃×#509	1	1	yes	characteristic
197	C₂²	C₁₃×#510	1	1	yes	characteristic
198	C₄	—	2	2	no	—
199	C₄	—	2	2	no	—
200	C₄	—	8	2	no	—
201	C₄	—	8	2	no	—
202	C₄	—	8	4	no	—
203	C₄	C₁₃×#391	1	1	yes	characteristic
204	C₄	C₁₃×#419	1	1	yes	characteristic
205	C₄	C₁₃×#475	1	2	yes	—
206	C₂	C₁₃×#1988	1	1	yes	characteristic
207	C₂	C₁₃×#2138	1	1	yes	characteristic
208	C₂	C₁₃×#2139	1	1	yes	characteristic
209	C₂	C₁₃×#2228	1	2	yes	—
210	C₂	C₁₃×#2229	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×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
9. C₁₃×#499	C₄	semidirect
41. #13277	C₁₃	direct (N × H)
96. #499	C₄×C₁₃	semidirect
170. C₁₃	#13277	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×#499	2
C₂×C₁₃×C₄⋊C₁₆	2
C₄×C₁₃×#107	2
C₁₃×#1380	2
#13277	13

Subgroups — C13×#13277 #15699616

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13277 #15699616