Subgroups — C₂×C₁₃×#2245 #15720039

Order 3328.

582 conjugacy classes of subgroups.

The subgroup lattice has 192 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×#494	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2245	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₁₃×#358	C₂	1	4	yes	maximal
5	C₂×C₁₃×#346	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×Q₁₆	—	2	1	no	—
7	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
8	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
9	C₂×C₁₃×#125	—	2	1	no	—
10	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
11	C₁₃×#499	—	2	2	no	—
12	C₁₃×#499	C₂²	1	4	yes	—
13	C₁₃×#494	—	2	2	no	—
14	C₁₃×#494	C₂²	1	4	yes	—
15	C₂×C₁₃×#107	C₂²	1	2	yes	—
16	C₂×C₁₃×#106	—	2	1	no	—
17	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#358	C₂²	1	16	yes	—
19	C₁₃×#346	C₂²	1	4	yes	—
20	C₂²×Q₈×C₁₃	—	2	2	no	—
21	C₂×C₁₃×Q₁₆	—	2	2	no	—
22	C₂×C₁₃×Q₁₆	—	2	4	no	—
23	C₂×C₁₃×Q₁₆	—	2	8	no	—
24	C₂×C₁₃×Q₁₆	—	4	4	no	—
25	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
26	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
28	C₁₃×C₄⋊Q₈	—	2	4	no	—
29	C₁₃×C₄⋊Q₈	—	4	2	no	—
30	C₁₃×#125	—	2	4	no	—
31	C₁₃×#125	—	4	2	no	—
32	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
33	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
34	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
35	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
36	C₂×C₁₃×C₁₆	—	2	4	no	—
37	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
38	C₁₃×#107	—	2	2	no	—
39	C₁₃×#107	C₂³	1	4	yes	—
40	C₁₃×#106	—	2	4	no	—
41	C₄×C₈×C₁₃	D₄	1	2	yes	—
42	C₄×C₈×C₁₃	C₂³	1	2	yes	—
43	C₂×#2245	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×Q₈×C₁₃	—	2	4	no	—
45	C₂×Q₈×C₁₃	—	4	2	no	—
46	C₂×Q₈×C₁₃	—	4	4	no	—
47	C₂×Q₈×C₁₃	—	4	4	no	—
48	C₂²×C₄×C₁₃	—	4	2	no	—
49	C₂²×C₄×C₁₃	—	4	2	no	—
50	C₂²×C₄×C₁₃	D₈	1	2	yes	—
51	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
52	C₁₃×Q₁₆	—	2	8	no	—
53	C₁₃×Q₁₆	—	4	4	no	—
54	C₁₃×Q₁₆	—	4	8	no	—
55	C₂×C₈×C₁₃	SD₁₆	1	4	yes	—
56	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
57	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
58	C₂×C₈×C₁₃	#41	1	4	yes	—
59	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
60	C₁₃×C₄⋊C₄	—	2	4	no	—
61	C₁₃×C₄⋊C₄	—	4	2	no	—
62	C₁₃×C₄⋊C₄	—	4	8	no	—
63	C₁₃×C₄⋊C₄	—	4	8	no	—
64	C₄²×C₁₃	D₈	1	2	yes	—
65	C₄²×C₁₃	C₂×D₄	1	2	yes	—
66	C₁₃×C₁₆	—	2	4	no	—
67	C₂×#499	C₂×C₁₃	1	1	yes	characteristic
68	C₂×#494	C₂×C₁₃	1	1	yes	characteristic
69	#2245	C₂×C₁₃	1	8	yes	direct product factor
70	C₂×#358	C₂×C₁₃	1	4	yes	—
71	C₂×#346	C₂×C₁₃	1	1	yes	characteristic
72	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
73	Q₈×C₁₃	—	4	4	no	—
74	Q₈×C₁₃	—	4	4	no	—
75	Q₈×C₁₃	—	8	4	no	—
76	C₂×C₄×C₁₃	—	2	4	no	—
77	C₂×C₄×C₁₃	—	4	4	no	—
78	C₂×C₄×C₁₃	—	4	4	no	—
79	C₂×C₄×C₁₃	—	8	4	no	—
80	C₂×C₄×C₁₃	—	8	4	no	—
81	C₂×C₄×C₁₃	#124	1	2	yes	—
82	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
83	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
84	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
85	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
86	C₈×C₁₃	#124	1	2	yes	—
87	C₈×C₁₃	C₂×SD₁₆	1	4	yes	—
88	C₈×C₁₃	C₂×#41	1	2	yes	—
89	C₂²×Q₁₆	—	2	1	no	—
90	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
91	C₂×C₄⋊Q₈	—	2	1	no	—
92	C₂×#125	—	2	1	no	—
93	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
94	#499	—	2	2	no	—
95	#499	C₂²×C₁₃	1	4	yes	—
96	#494	—	2	2	no	—
97	#494	C₂²×C₁₃	1	4	yes	—
98	C₂×#107	C₂²×C₁₃	1	2	yes	—
99	C₂×#106	—	2	1	no	—
100	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
101	#358	C₂²×C₁₃	1	16	yes	—
102	#346	C₂²×C₁₃	1	4	yes	—
103	C₂²×C₁₃	#486	1	2	yes	—
104	C₂²×C₁₃	#510	1	4	yes	—
105	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
106	C₄×C₁₃	—	2	4	no	—
107	C₄×C₁₃	—	8	4	no	—
108	C₄×C₁₃	—	8	4	no	—
109	C₄×C₁₃	#486	1	2	yes	—
110	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
111	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
112	C₂²×Q₈	—	2	2	no	—
113	C₂×Q₁₆	—	2	4	no	—
114	C₂×Q₁₆	—	2	2	no	—
115	C₂×Q₁₆	—	2	8	no	—
116	C₂×Q₁₆	—	4	4	no	—
117	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
118	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
119	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
120	C₄⋊Q₈	—	2	4	no	—
121	C₄⋊Q₈	—	4	2	no	—
122	#125	—	2	4	no	—
123	#125	—	4	2	no	—
124	C₂×C₄⋊C₄	—	2	2	no	—
125	C₂×C₄⋊C₄	—	4	2	no	—
126	C₂×C₄⋊C₄	—	4	2	no	—
127	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
128	C₂×C₁₆	—	2	4	no	—
129	C₂×C₁₆	C₂³×C₁₃	1	4	yes	—
130	#107	—	2	2	no	—
131	#107	C₂³×C₁₃	1	4	yes	—
132	#106	—	2	4	no	—
133	C₄×C₈	D₄×C₁₃	1	2	yes	—
134	C₄×C₈	C₂³×C₁₃	1	2	yes	—
135	C₂×C₁₃	#2245	1	4	yes	direct product factor
136	C₂×C₁₃	C₂×#486	1	1	yes	characteristic
137	C₂×C₁₃	C₂×#510	1	2	yes	—
138	C₂×Q₈	—	2	4	no	—
139	C₂×Q₈	—	4	2	no	—
140	C₂×Q₈	—	4	4	no	—
141	C₂×Q₈	—	4	4	no	—
142	C₂²×C₄	—	4	2	no	—
143	C₂²×C₄	—	4	2	no	—
144	C₂²×C₄	C₁₃×D₈	1	2	yes	—
145	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
146	Q₁₆	—	2	8	no	—
147	Q₁₆	—	4	4	no	—
148	Q₁₆	—	4	8	no	—
149	C₂×C₈	C₁₃×SD₁₆	1	4	yes	—
150	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
151	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
152	C₂×C₈	C₁₃×#41	1	4	yes	—
153	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
154	C₄⋊C₄	—	2	4	no	—
155	C₄⋊C₄	—	4	2	no	—
156	C₄⋊C₄	—	4	8	no	—
157	C₄⋊C₄	—	4	8	no	—
158	C₄²	C₁₃×D₈	1	2	yes	—
159	C₄²	C₂×D₄×C₁₃	1	2	yes	—
160	C₁₆	—	2	4	no	—
161	C₁₃	C₂×#2245	1	1	yes	characteristic, direct product factor, Sylow
162	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
163	Q₈	—	4	4	no	—
164	Q₈	—	4	4	no	—
165	Q₈	—	8	4	no	—
166	C₂×C₄	—	2	4	no	—
167	C₂×C₄	—	4	4	no	—
168	C₂×C₄	—	4	4	no	—
169	C₂×C₄	—	8	4	no	—
170	C₂×C₄	—	8	4	no	—
171	C₂×C₄	C₁₃×#124	1	2	yes	—
172	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
173	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
174	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
175	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
176	C₈	C₁₃×#124	1	2	yes	—
177	C₈	C₂×C₁₃×SD₁₆	1	4	yes	—
178	C₈	C₂×C₁₃×#41	1	2	yes	—
179	C₂²	C₁₃×#486	1	2	yes	—
180	C₂²	C₁₃×#510	1	4	yes	—
181	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
182	C₄	—	2	4	no	—
183	C₄	—	8	4	no	—
184	C₄	—	8	4	no	—
185	C₄	C₁₃×#486	1	2	yes	—
186	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
187	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
188	C₂	C₁₃×#2245	1	4	yes	direct product factor
189	C₂	C₂×C₁₃×#486	1	1	yes	characteristic
190	C₂	C₂×C₁₃×#510	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×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
3. C₁₃×#2245	C₂	direct (N × H)
43. C₂×#2245	C₁₃	direct (N × H)
69. #2245	C₂×C₁₃	direct (N × H)
135. C₂×C₁₃	#2245	direct (N × H)
161. C₁₃	C₂×#2245	direct (N × H)
188. C₂	C₁₃×#2245	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×#494	2
C₁₃×#2245	2
C₂×C₁₃×#358	2
C₂×C₁₃×#346	2
C₂×#2245	13

Subgroups — C2×C13×#2245 #15720039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2245 #15720039