Subgroups — C₁₃×#23801 #15710140

Order 3328.

986 conjugacy classes of subgroups.

The subgroup lattice has 186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×Q₁₆	C₂	1	4	yes	maximal
2	C₄×C₁₃×C₄⋊Q₈	C₂	1	2	yes	maximal
3	C₁₃×#2095	C₂	1	4	yes	maximal
4	C₁₃×#2016	C₂	1	4	yes	maximal
5	C₁₃×#1744	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	—
7	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
9	C₄×C₁₃×Q₁₆	—	2	16	no	—
10	C₂×C₁₃×#107	C₂²	1	4	yes	—
11	C₂×C₁₃×#103	C₂²	1	8	yes	—
12	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
13	C₁₃×#391	C₂²	1	4	yes	—
14	C₁₃×#389	—	2	4	no	—
15	C₁₃×#384	C₂²	1	2	yes	—
16	C₄×C₁₃×C₄⋊C₄	—	2	4	no	—
17	C₄³×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#336	C₂²	1	4	yes	—
19	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
20	C₂×C₁₃×Q₁₆	—	2	16	no	—
21	C₂×C₁₃×Q₁₆	—	2	8	no	—
22	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
23	C₁₃×C₄⋊Q₈	—	2	8	no	—
24	C₄×Q₈×C₁₃	—	2	16	no	—
25	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
28	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
29	C₂×C₄²×C₁₃	—	2	4	no	—
30	C₂×C₄²×C₁₃	D₄	1	2	yes	—
31	C₂×C₄²×C₁₃	D₄	1	2	yes	—
32	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
33	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
34	C₁₃×#107	—	2	8	no	—
35	C₁₃×#103	—	2	16	no	—
36	C₄×C₈×C₁₃	D₄	1	8	yes	—
37	C₁₃×#95	—	2	8	no	—
38	#23801	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂×Q₈×C₁₃	—	2	4	no	—
40	C₂×Q₈×C₁₃	—	2	8	no	—
41	C₂×Q₈×C₁₃	—	2	8	no	—
42	C₂×Q₈×C₁₃	#41	1	8	yes	—
43	C₂²×C₄×C₁₃	—	2	4	no	—
44	C₂²×C₄×C₁₃	—	2	4	no	—
45	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
47	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
49	C₁₃×Q₁₆	—	2	32	no	—
50	C₂×C₈×C₁₃	—	2	8	no	—
51	C₂×C₈×C₁₃	C₂×D₄	1	8	yes	—
52	C₁₃×C₄⋊C₄	—	2	16	no	—
53	C₁₃×C₄⋊C₄	—	2	8	no	—
54	C₁₃×C₄⋊C₄	—	4	8	no	—
55	C₁₃×C₄⋊C₄	—	4	8	no	—
56	C₄²×C₁₃	—	2	4	no	—
57	C₄²×C₁₃	—	4	2	no	—
58	C₄²×C₁₃	—	4	8	no	—
59	C₄²×C₁₃	Q₁₆	1	8	yes	complemented
60	C₄²×C₁₃	C₂×D₄	1	4	yes	—
61	C₂×C₄×Q₁₆	C₂×C₁₃	1	4	yes	—
62	C₄×C₄⋊Q₈	C₂×C₁₃	1	2	yes	—
63	#2095	C₂×C₁₃	1	4	yes	—
64	#2016	C₂×C₁₃	1	4	yes	—
65	#1744	C₂×C₁₃	1	1	yes	characteristic
66	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
67	Q₈×C₁₃	—	2	16	no	—
68	Q₈×C₁₃	—	4	8	no	—
69	C₂×C₄×C₁₃	—	2	4	no	—
70	C₂×C₄×C₁₃	—	2	4	no	—
71	C₂×C₄×C₁₃	—	2	2	no	—
72	C₂×C₄×C₁₃	—	2	8	no	—
73	C₂×C₄×C₁₃	—	4	4	no	—
74	C₂×C₄×C₁₃	—	4	4	no	—
75	C₂×C₄×C₁₃	—	4	4	no	—
76	C₂×C₄×C₁₃	—	4	8	no	—
77	C₂×C₄×C₁₃	#127	1	2	yes	—
78	C₂×C₄×C₁₃	#127	1	2	yes	—
79	C₂×C₄×C₁₃	C₂×Q₁₆	1	8	yes	—
80	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
81	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
82	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
83	C₈×C₁₃	—	2	8	no	—
84	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	—
85	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
86	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
87	C₄×Q₁₆	—	2	16	no	—
88	C₂×#107	C₂²×C₁₃	1	4	yes	—
89	C₂×#103	C₂²×C₁₃	1	8	yes	—
90	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
91	#391	C₂²×C₁₃	1	4	yes	—
92	#389	—	2	4	no	—
93	#384	C₂²×C₁₃	1	2	yes	—
94	C₄×C₄⋊C₄	—	2	4	no	—
95	C₄³	C₂²×C₁₃	1	1	yes	characteristic
96	#336	C₂²×C₁₃	1	4	yes	—
97	C₂²×C₁₃	#525	1	2	yes	—
98	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
99	C₂²×C₁₃	C₂²×Q₁₆	1	2	yes	—
100	C₂²×C₁₃	#575	1	2	yes	—
101	C₄×C₁₃	—	2	8	no	—
102	C₄×C₁₃	—	2	2	no	—
103	C₄×C₁₃	—	4	8	no	—
104	C₄×C₁₃	—	8	4	no	—
105	C₄×C₁₃	#494	1	4	yes	—
106	C₄×C₁₃	#525	1	4	yes	—
107	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
108	C₂×Q₁₆	—	2	16	no	—
109	C₂×Q₁₆	—	2	8	no	—
110	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
111	C₄⋊Q₈	—	2	8	no	—
112	C₄×Q₈	—	2	16	no	—
113	C₂×C₄⋊C₄	—	2	4	no	—
114	C₂×C₄⋊C₄	—	2	4	no	—
115	C₂×C₄⋊C₄	—	2	4	no	—
116	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
117	C₂×C₄²	—	2	4	no	—
118	C₂×C₄²	D₄×C₁₃	1	2	yes	—
119	C₂×C₄²	D₄×C₁₃	1	2	yes	—
120	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
121	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
122	#107	—	2	8	no	—
123	#103	—	2	16	no	—
124	C₄×C₈	D₄×C₁₃	1	8	yes	—
125	#95	—	2	8	no	—
126	C₂×C₁₃	#2397	1	1	yes	characteristic
127	C₂×C₁₃	#3104	1	4	yes	—
128	C₂×C₁₃	C₂×#494	1	1	yes	characteristic
129	C₂×C₁₃	#3150	1	1	yes	characteristic
130	C₂×Q₈	—	2	4	no	—
131	C₂×Q₈	—	2	8	no	—
132	C₂×Q₈	—	2	8	no	—
133	C₂×Q₈	C₁₃×#41	1	8	yes	—
134	C₂²×C₄	—	2	4	no	—
135	C₂²×C₄	—	2	4	no	—
136	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
137	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
138	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
139	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
140	Q₁₆	—	2	32	no	—
141	C₂×C₈	—	2	8	no	—
142	C₂×C₈	C₂×D₄×C₁₃	1	8	yes	—
143	C₄⋊C₄	—	2	16	no	—
144	C₄⋊C₄	—	2	8	no	—
145	C₄⋊C₄	—	4	8	no	—
146	C₄⋊C₄	—	4	8	no	—
147	C₄²	—	2	4	no	—
148	C₄²	—	4	2	no	—
149	C₄²	—	4	8	no	—
150	C₄²	C₁₃×Q₁₆	1	8	yes	complemented
151	C₄²	C₂×D₄×C₁₃	1	4	yes	—
152	C₁₃	#23801	1	1	yes	characteristic, direct product factor, Sylow
153	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
154	Q₈	—	2	16	no	—
155	Q₈	—	4	8	no	—
156	C₂×C₄	—	2	4	no	—
157	C₂×C₄	—	2	4	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	8	no	—
160	C₂×C₄	—	4	4	no	—
161	C₂×C₄	—	4	4	no	—
162	C₂×C₄	—	4	4	no	—
163	C₂×C₄	—	4	8	no	—
164	C₂×C₄	C₁₃×#127	1	2	yes	—
165	C₂×C₄	C₁₃×#127	1	2	yes	—
166	C₂×C₄	C₂×C₁₃×Q₁₆	1	8	yes	—
167	C₂×C₄	C₂×C₁₃×Q₁₆	1	4	yes	—
168	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
169	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
170	C₈	—	2	8	no	—
171	C₂²	C₁₃×#525	1	2	yes	—
172	C₂²	C₂×C₁₃×#127	1	1	yes	characteristic
173	C₂²	C₂²×C₁₃×Q₁₆	1	2	yes	—
174	C₂²	C₁₃×#575	1	2	yes	—
175	C₄	—	2	8	no	—
176	C₄	—	2	2	no	—
177	C₄	—	4	8	no	—
178	C₄	—	8	4	no	—
179	C₄	C₁₃×#494	1	4	yes	—
180	C₄	C₁₃×#525	1	4	yes	—
181	C₂	C₁₃×#2397	1	1	yes	characteristic
182	C₂	C₁₃×#3104	1	4	yes	—
183	C₂	C₂×C₁₃×#494	1	1	yes	characteristic
184	C₂	C₁₃×#3150	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle, prime radical	C₂³×C₁₃	C₂²×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
38. #23801	C₁₃	direct (N × H)
59. C₄²×C₁₃	Q₁₆	semidirect
150. C₄²	C₁₃×Q₁₆	semidirect
152. C₁₃	#23801	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×C₄×C₁₃×Q₁₆	2
C₄×C₁₃×C₄⋊Q₈	2
C₁₃×#2095	2
C₁₃×#2016	2
C₁₃×#1744	2
#23801	13

Subgroups — C13×#23801 #15710140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23801 #15710140