Subgroups — C₁₃×#13284 #15699623

Order 3328.

374 conjugacy classes of subgroups.

The subgroup lattice has 182 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×#346	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1380	C₂	1	4	yes	maximal
5	C₂×C₁₃×#125	—	2	1	no	—
6	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
7	C₁₃×#499	—	2	2	no	—
8	C₁₃×#499	C₄	1	4	yes	complemented
9	C₂×C₁₃×#107	—	2	1	no	—
10	C₂×C₁₃×#107	C₂²	1	2	yes	—
11	C₂×C₁₃×#107	C₂²	1	2	yes	—
12	C₂×C₁₃×#106	—	2	1	no	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#384	—	2	1	no	—
15	C₁₃×#346	—	2	2	no	—
16	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
18	C₁₃×#125	—	2	4	no	—
19	C₁₃×#125	—	4	2	no	—
20	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
21	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
22	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
23	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
24	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
25	C₂×C₁₃×C₁₆	—	2	2	no	—
26	C₂×C₁₃×C₁₆	—	2	2	no	—
27	C₂×C₁₃×C₁₆	Q₈	1	4	yes	—
28	C₁₃×#107	—	2	2	no	—
29	C₁₃×#107	—	2	4	no	—
30	C₁₃×#107	—	4	2	no	—
31	C₁₃×#107	C₂×C₄	1	4	yes	—
32	C₁₃×#106	—	2	4	no	—
33	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
34	C₄×C₈×C₁₃	D₄	1	2	yes	—
35	#13284	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂²×C₄×C₁₃	—	4	2	no	—
37	C₂²×C₄×C₁₃	—	4	2	no	—
38	C₂²×C₄×C₁₃	D₈	1	2	yes	—
39	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
40	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
41	C₂×C₈×C₁₃	SD₁₆	1	2	yes	—
42	C₂×C₈×C₁₃	Q₁₆	1	2	yes	—
43	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
45	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
46	C₂×C₈×C₁₃	#41	1	2	yes	—
47	C₁₃×C₄⋊C₄	—	2	4	no	—
48	C₁₃×C₄⋊C₄	—	4	8	no	—
49	C₁₃×C₄⋊C₄	—	4	2	no	—
50	C₁₃×C₄⋊C₄	—	4	2	no	—
51	C₁₃×C₄⋊C₄	—	4	2	no	—
52	C₁₃×C₄⋊C₄	—	8	4	no	—
53	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
54	C₄²×C₁₃	SD₁₆	1	2	yes	—
55	C₁₃×C₁₆	—	2	4	no	—
56	C₂×#499	C₂×C₁₃	1	1	yes	characteristic
57	C₂×#346	C₂×C₁₃	1	1	yes	characteristic
58	#1845	C₂×C₁₃	1	1	yes	characteristic
59	#1380	C₂×C₁₃	1	4	yes	—
60	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
61	C₂×C₄×C₁₃	—	2	2	no	—
62	C₂×C₄×C₁₃	—	2	2	no	—
63	C₂×C₄×C₁₃	—	4	4	no	—
64	C₂×C₄×C₁₃	—	8	2	no	—
65	C₂×C₄×C₁₃	—	8	2	no	—
66	C₂×C₄×C₁₃	—	8	2	no	—
67	C₂×C₄×C₁₃	—	8	4	no	—
68	C₂×C₄×C₁₃	#102	1	4	yes	—
69	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
71	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
72	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
73	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
74	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
75	C₈×C₁₃	#103	1	4	yes	—
76	C₈×C₁₃	C₄×Q₈	1	2	yes	—
77	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
78	C₂×#125	—	2	1	no	—
79	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
80	#499	—	2	2	no	—
81	#499	C₄×C₁₃	1	4	yes	complemented
82	C₂×#107	—	2	1	no	—
83	C₂×#107	C₂²×C₁₃	1	2	yes	—
84	C₂×#107	C₂²×C₁₃	1	2	yes	—
85	C₂×#106	—	2	1	no	—
86	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
87	#384	—	2	1	no	—
88	#346	—	2	2	no	—
89	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
90	C₂²×C₁₃	#486	1	1	yes	characteristic
91	C₂²×C₁₃	#500	1	1	yes	characteristic
92	C₂²×C₁₃	#509	1	2	yes	—
93	C₂²×C₁₃	#510	1	2	yes	—
94	C₄×C₁₃	—	2	4	no	—
95	C₄×C₁₃	—	8	4	no	—
96	C₄×C₁₃	—	16	2	no	—
97	C₄×C₁₃	#391	1	1	yes	characteristic
98	C₄×C₁₃	C₂×#103	1	1	yes	characteristic
99	C₄×C₁₃	#487	1	1	yes	characteristic
100	C₄×C₁₃	#498	1	1	yes	characteristic
101	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
102	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
103	#125	—	2	4	no	—
104	#125	—	4	2	no	—
105	C₂×C₄⋊C₄	—	2	2	no	—
106	C₂×C₄⋊C₄	—	2	2	no	—
107	C₂×C₄⋊C₄	—	4	2	no	—
108	C₂×C₄⋊C₄	—	4	2	no	—
109	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
110	C₂×C₁₆	—	2	2	no	—
111	C₂×C₁₆	—	2	2	no	—
112	C₂×C₁₆	Q₈×C₁₃	1	4	yes	—
113	#107	—	2	2	no	—
114	#107	—	2	4	no	—
115	#107	—	4	2	no	—
116	#107	C₂×C₄×C₁₃	1	4	yes	—
117	#106	—	2	4	no	—
118	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
119	C₄×C₈	D₄×C₁₃	1	2	yes	—
120	C₂×C₁₃	#1990	1	1	yes	characteristic
121	C₂×C₁₃	#2139	1	2	yes	—
122	C₂×C₁₃	#2244	1	1	yes	characteristic
123	C₂×C₁₃	#2245	1	1	yes	characteristic
124	C₂×C₁₃	#2255	1	2	yes	—
125	C₂²×C₄	—	4	2	no	—
126	C₂²×C₄	—	4	2	no	—
127	C₂²×C₄	C₁₃×D₈	1	2	yes	—
128	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
129	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
130	C₂×C₈	C₁₃×SD₁₆	1	2	yes	—
131	C₂×C₈	C₁₃×Q₁₆	1	2	yes	—
132	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
133	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
134	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
135	C₂×C₈	C₁₃×#41	1	2	yes	—
136	C₄⋊C₄	—	2	4	no	—
137	C₄⋊C₄	—	4	8	no	—
138	C₄⋊C₄	—	4	2	no	—
139	C₄⋊C₄	—	4	2	no	—
140	C₄⋊C₄	—	4	2	no	—
141	C₄⋊C₄	—	8	4	no	—
142	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
143	C₄²	C₁₃×SD₁₆	1	2	yes	—
144	C₁₆	—	2	4	no	—
145	C₁₃	#13284	1	1	yes	characteristic, direct product factor, Sylow
146	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	2	no	—
149	C₂×C₄	—	4	4	no	—
150	C₂×C₄	—	8	2	no	—
151	C₂×C₄	—	8	2	no	—
152	C₂×C₄	—	8	2	no	—
153	C₂×C₄	—	8	4	no	—
154	C₂×C₄	C₁₃×#102	1	4	yes	—
155	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
157	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
158	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
159	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
160	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
161	C₈	C₁₃×#103	1	4	yes	—
162	C₈	C₄×Q₈×C₁₃	1	2	yes	—
163	C₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
164	C₂²	C₂×C₁₃×#102	1	1	yes	characteristic
165	C₂²	C₁₃×#486	1	1	yes	characteristic
166	C₂²	C₁₃×#500	1	1	yes	characteristic
167	C₂²	C₁₃×#509	1	2	yes	—
168	C₂²	C₁₃×#510	1	2	yes	—
169	C₄	—	2	4	no	—
170	C₄	—	8	4	no	—
171	C₄	—	16	2	no	—
172	C₄	C₁₃×#391	1	1	yes	characteristic
173	C₄	C₂×C₁₃×#103	1	1	yes	characteristic
174	C₄	C₁₃×#487	1	1	yes	characteristic
175	C₄	C₁₃×#498	1	1	yes	characteristic
176	C₂	C₁₃×#1990	1	1	yes	characteristic
177	C₂	C₁₃×#2139	1	2	yes	—
178	C₂	C₁₃×#2244	1	1	yes	characteristic
179	C₂	C₁₃×#2245	1	1	yes	characteristic
180	C₂	C₁₃×#2255	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
8. C₁₃×#499	C₄	semidirect
35. #13284	C₁₃	direct (N × H)
81. #499	C₄×C₁₃	semidirect
145. C₁₃	#13284	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×#346	2
C₁₃×#1845	2
C₁₃×#1380	2
#13284	13

Subgroups — C13×#13284 #15699623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13284 #15699623