Subgroups — C₁₃×#2584 #13111642

Order 1664.

468 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×#125	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#398	C₂	1	2	yes	maximal
4	C₁₃×#395	C₂	1	2	yes	maximal
5	C₁₃×#389	C₂	1	2	yes	maximal
6	C₁₃×#389	C₂	1	4	yes	maximal
7	C₁₃×#389	C₂	1	2	yes	maximal
8	C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₁₃×#125	—	2	4	no	—
11	C₄×Q₈×C₁₃	—	2	4	no	—
12	C₂×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
13	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
20	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
22	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
23	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#95	C₂²	1	2	yes	—
25	C₁₃×#95	C₂²	1	4	yes	—
26	C₁₃×#95	C₂²	1	4	yes	—
27	C₂×Q₈×C₁₃	—	2	2	no	—
28	C₂×Q₈×C₁₃	—	2	4	no	—
29	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
30	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
31	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
32	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
33	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
34	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
35	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
36	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
37	C₁₃×C₄⋊C₄	—	2	4	no	—
38	C₁₃×C₄⋊C₄	—	2	2	no	—
39	C₁₃×C₄⋊C₄	—	2	4	no	—
40	C₁₃×C₄⋊C₄	—	2	4	no	—
41	C₁₃×C₄⋊C₄	—	2	2	no	—
42	C₁₃×C₄⋊C₄	—	2	2	no	—
43	C₁₃×C₄⋊C₄	—	2	8	no	—
44	C₁₃×C₄⋊C₄	—	4	4	no	—
45	C₁₃×C₄⋊C₄	Q₈	1	8	yes	complemented
46	C₄²×C₁₃	—	2	4	no	—
47	C₄²×C₁₃	—	4	2	no	—
48	C₄²×C₁₃	D₄	1	4	yes	—
49	#2584	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
51	Q₈×C₁₃	—	2	8	no	—
52	C₂×C₄×C₁₃	—	2	2	no	—
53	C₂×C₄×C₁₃	—	2	4	no	—
54	C₂×C₄×C₁₃	—	2	2	no	—
55	C₂×C₄×C₁₃	—	2	2	no	—
56	C₂×C₄×C₁₃	—	2	1	no	—
57	C₂×C₄×C₁₃	—	2	4	no	—
58	C₂×C₄×C₁₃	—	2	1	no	—
59	C₂×C₄×C₁₃	—	2	2	no	—
60	C₂×C₄×C₁₃	—	2	2	no	—
61	C₂×C₄×C₁₃	—	2	2	no	—
62	C₂×C₄×C₁₃	—	2	4	no	—
63	C₂×C₄×C₁₃	—	2	2	no	—
64	C₂×C₄×C₁₃	—	2	2	no	—
65	C₂×C₄×C₁₃	—	2	2	no	—
66	C₂×C₄×C₁₃	—	2	2	no	—
67	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
68	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
69	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
70	C₂×C₄×C₁₃	C₂×Q₈	1	8	yes	—
71	C₂×C₄×C₁₃	C₂×Q₈	1	4	yes	—
72	C₂×C₄×C₁₃	#41	1	4	yes	—
73	C₂×#125	C₂×C₁₃	1	1	yes	characteristic
74	C₂×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic
75	#398	C₂×C₁₃	1	2	yes	—
76	#395	C₂×C₁₃	1	2	yes	—
77	#389	C₂×C₁₃	1	2	yes	—
78	#389	C₂×C₁₃	1	4	yes	—
79	#389	C₂×C₁₃	1	2	yes	—
80	C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
81	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
82	C₂²×C₁₃	C₂²×Q₈	1	2	yes	—
83	C₂²×C₁₃	C₂×#41	1	2	yes	—
84	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
85	C₂²×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
86	C₄×C₁₃	—	2	2	no	—
87	C₄×C₁₃	—	2	4	no	—
88	C₄×C₁₃	—	2	2	no	—
89	C₄×C₁₃	—	2	8	no	—
90	C₄×C₁₃	—	4	2	no	—
91	C₄×C₁₃	—	4	2	no	—
92	C₄×C₁₃	—	4	2	no	—
93	C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
94	C₂²×Q₈	C₂²×C₁₃	1	1	yes	characteristic
95	#125	—	2	4	no	—
96	C₄×Q₈	—	2	4	no	—
97	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
98	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
99	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
100	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
101	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
102	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
103	C₂×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
104	C₂×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
105	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
106	C₂×C₄²	C₂²×C₁₃	1	2	yes	—
107	C₂×C₄²	C₂²×C₁₃	1	2	yes	—
108	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
109	#95	C₂²×C₁₃	1	2	yes	—
110	#95	C₂²×C₁₃	1	4	yes	—
111	#95	C₂²×C₁₃	1	4	yes	—
112	C₂×C₁₃	#525	1	1	yes	characteristic
113	C₂×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
114	C₂×C₁₃	#537	1	1	yes	characteristic
115	C₂×C₁₃	#554	1	2	yes	—
116	C₂×C₁₃	#557	1	2	yes	—
117	C₂×Q₈	—	2	2	no	—
118	C₂×Q₈	—	2	4	no	—
119	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
120	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
121	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
122	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
123	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
124	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
125	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
126	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
127	C₄⋊C₄	—	2	4	no	—
128	C₄⋊C₄	—	2	2	no	—
129	C₄⋊C₄	—	2	4	no	—
130	C₄⋊C₄	—	2	4	no	—
131	C₄⋊C₄	—	2	2	no	—
132	C₄⋊C₄	—	2	2	no	—
133	C₄⋊C₄	—	2	8	no	—
134	C₄⋊C₄	—	4	4	no	—
135	C₄⋊C₄	Q₈×C₁₃	1	8	yes	complemented
136	C₄²	—	2	4	no	—
137	C₄²	—	4	2	no	—
138	C₄²	D₄×C₁₃	1	4	yes	—
139	C₁₃	#2584	1	1	yes	characteristic, direct product factor, Sylow
140	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
141	Q₈	—	2	8	no	—
142	C₂×C₄	—	2	2	no	—
143	C₂×C₄	—	2	4	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	2	1	no	—
147	C₂×C₄	—	2	4	no	—
148	C₂×C₄	—	2	1	no	—
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	2	4	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	2	2	no	—
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
158	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
159	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
160	C₂×C₄	C₂×Q₈×C₁₃	1	8	yes	—
161	C₂×C₄	C₂×Q₈×C₁₃	1	4	yes	—
162	C₂×C₄	C₁₃×#41	1	4	yes	—
163	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
164	C₂²	C₂²×Q₈×C₁₃	1	2	yes	—
165	C₂²	C₂×C₁₃×#41	1	2	yes	—
166	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
167	C₂²	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
168	C₄	—	2	2	no	—
169	C₄	—	2	4	no	—
170	C₄	—	2	2	no	—
171	C₄	—	2	8	no	—
172	C₄	—	4	2	no	—
173	C₄	—	4	2	no	—
174	C₄	—	4	2	no	—
175	C₄	C₁₃×C₄⋊Q₈	1	4	yes	—
176	C₂	C₁₃×#525	1	1	yes	characteristic
177	C₂	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
178	C₂	C₁₃×#537	1	1	yes	characteristic
179	C₂	C₁₃×#554	1	2	yes	—
180	C₂	C₁₃×#557	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
45. C₁₃×C₄⋊C₄	Q₈	semidirect
49. #2584	C₁₃	direct (N × H)
135. C₄⋊C₄	Q₈×C₁₃	semidirect
139. C₁₃	#2584	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×#125	2
C₂×C₄×Q₈×C₁₃	2
C₁₃×#398	2
C₁₃×#395	2
C₁₃×#389	2
C₄×C₁₃×C₄⋊C₄	2
#2584	13

Subgroups — C13×#2584 #13111642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2584 #13111642