Subgroups — C₂×C₁₃×#2859 #15722967

Order 3328.

2558 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	C₂²×C₁₃×#125	C₂	1	2	yes	maximal
2	C₁₃×#2859	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#389	C₂	1	8	yes	maximal
4	C₂×C₁₃×#384	C₂	1	2	yes	maximal
5	C₂×C₁₃×#382	C₂	1	2	yes	maximal
6	C₂×C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#125	—	2	16	no	—
8	C₂×C₁₃×#125	C₂²	1	16	yes	—
9	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
10	C₂²×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
11	C₂²×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
12	C₂²×C₄²×C₁₃	C₂²	1	4	yes	—
13	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#389	C₂²	1	64	yes	—
17	C₁₃×#384	C₂²	1	16	yes	—
18	C₁₃×#382	C₂²	1	16	yes	—
19	C₂×C₁₃×#95	C₂²	1	8	yes	—
20	C₄³×C₁₃	C₂²	1	8	yes	—
21	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
22	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
23	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
24	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
25	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
26	C₁₃×#125	—	2	64	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	32	no	—
28	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	32	no	—
30	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
31	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	—
32	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	—
33	C₂×C₄²×C₁₃	—	2	16	no	—
34	C₂×C₄²×C₁₃	D₄	1	8	yes	—
35	C₂×C₄²×C₁₃	Q₈	1	8	yes	—
36	C₂×C₄²×C₁₃	Q₈	1	8	yes	—
37	C₂×C₄²×C₁₃	C₂³	1	16	yes	—
38	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
39	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
40	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
41	C₁₃×#95	C₂³	1	32	yes	—
42	C₂×#2859	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
44	C₂²×C₄×C₁₃	—	2	8	no	—
45	C₂²×C₄×C₁₃	—	2	8	no	—
46	C₂²×C₄×C₁₃	—	2	16	no	—
47	C₂²×C₄×C₁₃	—	2	32	no	—
48	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
49	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
50	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
51	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
52	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
53	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
54	C₂²×C₄×C₁₃	#41	1	16	yes	—
55	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
56	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
57	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
58	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
59	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
60	C₁₃×C₄⋊C₄	—	2	64	no	—
61	C₁₃×C₄⋊C₄	—	2	32	no	—
62	C₁₃×C₄⋊C₄	—	2	64	no	—
63	C₄²×C₁₃	—	2	32	no	—
64	C₄²×C₁₃	C₂×D₄	1	16	yes	—
65	C₄²×C₁₃	C₂×Q₈	1	16	yes	—
66	C₄²×C₁₃	C₂×Q₈	1	16	yes	—
67	C₂²×#125	C₂×C₁₃	1	2	yes	—
68	#2859	C₂×C₁₃	1	16	yes	direct product factor
69	C₂×#389	C₂×C₁₃	1	8	yes	—
70	C₂×#384	C₂×C₁₃	1	2	yes	—
71	C₂×#382	C₂×C₁₃	1	2	yes	—
72	C₂×C₄³	C₂×C₁₃	1	1	yes	characteristic
73	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
74	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
75	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
76	C₂³×C₁₃	C₂×#41	1	8	yes	—
77	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
78	C₂×C₄×C₁₃	—	2	16	no	—
79	C₂×C₄×C₁₃	—	2	16	no	—
80	C₂×C₄×C₁₃	—	2	8	no	—
81	C₂×C₄×C₁₃	—	2	8	no	—
82	C₂×C₄×C₁₃	—	2	16	no	—
83	C₂×C₄×C₁₃	—	2	32	no	—
84	C₂×C₄×C₁₃	—	4	32	no	—
85	C₂×C₄×C₁₃	#125	1	32	yes	complemented
86	C₂×C₄×C₁₃	C₄⋊Q₈	1	16	yes	—
87	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
88	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
89	C₂×C₄×C₁₃	C₂²×Q₈	1	8	yes	—
90	C₂×C₄×C₁₃	C₂²×Q₈	1	8	yes	—
91	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
92	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
93	C₂×C₄×C₁₃	C₂×#41	1	16	yes	—
94	C₂×#125	—	2	16	no	—
95	C₂×#125	C₂²×C₁₃	1	16	yes	—
96	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
97	C₂²×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
98	C₂²×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
99	C₂²×C₄²	C₂²×C₁₃	1	4	yes	—
100	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
101	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
102	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
103	#389	C₂²×C₁₃	1	64	yes	—
104	#384	C₂²×C₁₃	1	16	yes	—
105	#382	C₂²×C₁₃	1	16	yes	—
106	C₂×#95	C₂²×C₁₃	1	8	yes	—
107	C₄³	C₂²×C₁₃	1	8	yes	—
108	C₂²×C₁₃	C₂×#125	1	8	yes	—
109	C₂²×C₁₃	C₂×C₄⋊Q₈	1	4	yes	—
110	C₂²×C₁₃	#532	1	8	yes	—
111	C₂²×C₁₃	#533	1	8	yes	—
112	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
113	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
114	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
115	C₂²×C₁₃	C₂²×#41	1	4	yes	—
116	C₄×C₁₃	—	2	8	no	—
117	C₄×C₁₃	—	2	8	no	—
118	C₄×C₁₃	—	4	16	no	—
119	C₄×C₁₃	C₂×#125	1	16	yes	complemented
120	C₄×C₁₃	C₂×C₄⋊Q₈	1	8	yes	—
121	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
122	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
123	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
124	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
125	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
126	#125	—	2	64	no	—
127	C₂×C₄⋊C₄	—	2	32	no	—
128	C₂×C₄⋊C₄	—	2	16	no	—
129	C₂×C₄⋊C₄	—	2	32	no	—
130	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
131	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	—
132	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	—
133	C₂×C₄²	—	2	16	no	—
134	C₂×C₄²	D₄×C₁₃	1	8	yes	—
135	C₂×C₄²	Q₈×C₁₃	1	8	yes	—
136	C₂×C₄²	Q₈×C₁₃	1	8	yes	—
137	C₂×C₄²	C₂³×C₁₃	1	16	yes	—
138	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
139	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
140	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
141	#95	C₂³×C₁₃	1	32	yes	—
142	C₂×C₁₃	#2859	1	8	yes	direct product factor
143	C₂×C₁₃	C₂²×#125	1	2	yes	—
144	C₂×C₁₃	C₂²×C₄⋊Q₈	1	1	yes	characteristic
145	C₂×C₁₃	C₂×#532	1	2	yes	—
146	C₂×C₁₃	C₂×#533	1	2	yes	—
147	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
148	C₂²×C₄	—	2	8	no	—
149	C₂²×C₄	—	2	8	no	—
150	C₂²×C₄	—	2	16	no	—
151	C₂²×C₄	—	2	32	no	—
152	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
153	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
154	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
155	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
156	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
157	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
158	C₂²×C₄	C₁₃×#41	1	16	yes	—
159	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
160	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
161	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
162	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
163	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
164	C₄⋊C₄	—	2	64	no	—
165	C₄⋊C₄	—	2	32	no	—
166	C₄⋊C₄	—	2	64	no	—
167	C₄²	—	2	32	no	—
168	C₄²	C₂×D₄×C₁₃	1	16	yes	—
169	C₄²	C₂×Q₈×C₁₃	1	16	yes	—
170	C₄²	C₂×Q₈×C₁₃	1	16	yes	—
171	C₁₃	C₂×#2859	1	1	yes	characteristic, direct product factor, Sylow
172	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
173	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
174	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
175	C₂³	C₂×C₁₃×#41	1	8	yes	—
176	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
177	C₂×C₄	—	2	16	no	—
178	C₂×C₄	—	2	16	no	—
179	C₂×C₄	—	2	8	no	—
180	C₂×C₄	—	2	8	no	—
181	C₂×C₄	—	2	16	no	—
182	C₂×C₄	—	2	32	no	—
183	C₂×C₄	—	4	32	no	—
184	C₂×C₄	C₁₃×#125	1	32	yes	complemented
185	C₂×C₄	C₁₃×C₄⋊Q₈	1	16	yes	—
186	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
187	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
188	C₂×C₄	C₂²×Q₈×C₁₃	1	8	yes	—
189	C₂×C₄	C₂²×Q₈×C₁₃	1	8	yes	—
190	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
191	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
192	C₂×C₄	C₂×C₁₃×#41	1	16	yes	—
193	C₂²	C₂×C₁₃×#125	1	8	yes	—
194	C₂²	C₂×C₁₃×C₄⋊Q₈	1	4	yes	—
195	C₂²	C₁₃×#532	1	8	yes	—
196	C₂²	C₁₃×#533	1	8	yes	—
197	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
198	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
199	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
200	C₂²	C₂²×C₁₃×#41	1	4	yes	—
201	C₄	—	2	8	no	—
202	C₄	—	2	8	no	—
203	C₄	—	4	16	no	—
204	C₄	C₂×C₁₃×#125	1	16	yes	complemented
205	C₄	C₂×C₁₃×C₄⋊Q₈	1	8	yes	—
206	C₂	C₁₃×#2859	1	8	yes	direct product factor
207	C₂	C₂²×C₁₃×#125	1	2	yes	—
208	C₂	C₂²×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
209	C₂	C₂×C₁₃×#532	1	2	yes	—
210	C₂	C₂×C₁₃×#533	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2859	C₂	direct (N × H)
42. C₂×#2859	C₁₃	direct (N × H)
68. #2859	C₂×C₁₃	direct (N × H)
85. C₂×C₄×C₁₃	#125	semidirect
119. C₄×C₁₃	C₂×#125	semidirect
142. C₂×C₁₃	#2859	direct (N × H)
171. C₁₃	C₂×#2859	direct (N × H)
184. C₂×C₄	C₁₃×#125	semidirect
204. C₄	C₂×C₁₃×#125	semidirect
206. C₂	C₁₃×#2859	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₃×#125	2
C₁₃×#2859	2
C₂×C₁₃×#389	2
C₂×C₁₃×#384	2
C₂×C₁₃×#382	2
C₂×C₄³×C₁₃	2
C₂×#2859	13

Subgroups — C2×C13×#2859 #15722967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2859 #15722967