Subgroups — C₁₃×#13853 #15700192

Order 3328.

1942 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal
3	C₁₃×#1445	C₂	1	4	yes	maximal, complemented
4	C₁₃×#1440	C₂	1	4	yes	maximal
5	C₄×C₁₃×#95	C₂	1	4	yes	maximal, complemented
6	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×#117	—	2	8	no	—
8	C₂×C₁₃×#117	C₄	1	8	yes	complemented
9	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
11	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
12	C₂²×C₄²×C₁₃	C₂²	1	4	yes	—
13	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
14	C₄×C₁₃×C₂²⋊C₄	—	2	8	no	—
15	C₂×C₁₃×#95	C₂²	1	4	yes	—
16	C₂×C₁₃×#95	C₂²	1	16	yes	—
17	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
18	C₂³×C₄×C₁₃	—	2	8	no	—
19	C₂³×C₄×C₁₃	C₂×C₄	1	4	yes	—
20	C₂³×C₄×C₁₃	D₄	1	8	yes	—
21	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
22	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
23	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
25	C₁₃×#117	—	2	32	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
28	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
29	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
30	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
31	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
32	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	8	yes	—
33	C₂×C₄²×C₁₃	—	2	8	no	—
34	C₂×C₄²×C₁₃	—	2	8	no	—
35	C₂×C₄²×C₁₃	—	2	16	no	—
36	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	—
37	C₁₃×#95	—	2	8	no	—
38	C₁₃×#95	—	2	32	no	—
39	#13853	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂⁴×C₁₃	—	2	8	no	—
41	C₂⁴×C₁₃	—	2	4	no	—
42	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
43	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
44	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
45	C₂²×C₄×C₁₃	—	2	4	no	—
46	C₂²×C₄×C₁₃	—	2	16	no	—
47	C₂²×C₄×C₁₃	—	2	32	no	—
48	C₂²×C₄×C₁₃	—	2	8	no	—
49	C₂²×C₄×C₁₃	—	2	4	no	—
50	C₂²×C₄×C₁₃	—	2	4	no	—
51	C₂²×C₄×C₁₃	—	2	16	no	—
52	C₂²×C₄×C₁₃	—	2	16	no	—
53	C₂²×C₄×C₁₃	—	2	16	no	—
54	C₂²×C₄×C₁₃	—	2	8	no	—
55	C₂²×C₄×C₁₃	C₂²⋊C₄	1	16	yes	—
56	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
57	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
58	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
59	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
60	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
61	C₂²×C₄×C₁₃	#41	1	16	yes	—
62	C₂²×C₄×C₁₃	#41	1	8	yes	—
63	C₁₃×C₄⋊C₄	—	2	16	no	—
64	C₁₃×C₂²⋊C₄	—	2	32	no	—
65	C₁₃×C₂²⋊C₄	—	2	16	no	—
66	C₄²×C₁₃	—	2	16	no	—
67	C₄²×C₁₃	—	4	16	no	—
68	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic
69	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	2	yes	—
70	#1445	C₂×C₁₃	1	4	yes	complemented
71	#1440	C₂×C₁₃	1	4	yes	—
72	C₄×#95	C₂×C₁₃	1	4	yes	complemented
73	C₂³×C₁₃	—	2	4	no	—
74	C₂³×C₁₃	—	2	8	no	—
75	C₂³×C₁₃	—	2	8	no	—
76	C₂³×C₁₃	—	2	8	no	—
77	C₂³×C₁₃	—	2	8	no	—
78	C₂³×C₁₃	—	4	16	no	—
79	C₂³×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
80	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
81	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
82	C₂³×C₁₃	C₂×#41	1	4	yes	—
83	C₂³×C₁₃	C₂×#41	1	8	yes	—
84	C₂×C₄×C₁₃	—	2	4	no	—
85	C₂×C₄×C₁₃	—	2	8	no	—
86	C₂×C₄×C₁₃	—	2	32	no	—
87	C₂×C₄×C₁₃	—	2	8	no	—
88	C₂×C₄×C₁₃	—	2	16	no	—
89	C₂×C₄×C₁₃	—	2	16	no	—
90	C₂×C₄×C₁₃	—	2	32	no	—
91	C₂×C₄×C₁₃	—	4	8	no	—
92	C₂×C₄×C₁₃	—	4	8	no	—
93	C₂×C₄×C₁₃	—	4	16	no	—
94	C₂×C₄×C₁₃	—	4	8	no	—
95	C₂×C₄×C₁₃	—	4	8	no	—
96	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
97	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
98	C₂×C₄×C₁₃	#117	1	8	yes	—
99	C₂×C₄×C₁₃	#123	1	16	yes	—
100	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
101	C₂×#117	—	2	8	no	—
102	C₂×#117	C₄×C₁₃	1	8	yes	complemented
103	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
104	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
105	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
106	C₂²×C₄²	C₂²×C₁₃	1	4	yes	—
107	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
108	C₄×C₂²⋊C₄	—	2	8	no	—
109	C₂×#95	C₂²×C₁₃	1	16	yes	—
110	C₂×#95	C₂²×C₁₃	1	4	yes	—
111	C₂²×C₁₃	—	2	4	no	—
112	C₂²×C₁₃	—	2	8	no	—
113	C₂²×C₁₃	—	4	16	no	—
114	C₂²×C₁₃	—	4	8	no	—
115	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₁₃	C₂×#117	1	2	yes	—
117	C₂²×C₁₃	C₄×#41	1	4	yes	—
118	C₂²×C₁₃	C₂×#123	1	4	yes	—
119	C₂²×C₁₃	#525	1	4	yes	—
120	C₂²×C₁₃	#529	1	16	yes	—
121	C₂²×C₁₃	#532	1	4	yes	—
122	C₄×C₁₃	—	2	4	no	—
123	C₄×C₁₃	—	4	16	no	—
124	C₄×C₁₃	—	4	8	no	—
125	C₄×C₁₃	#381	1	8	yes	—
126	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
127	C₂³×C₄	—	2	8	no	—
128	C₂³×C₄	C₂×C₄×C₁₃	1	4	yes	—
129	C₂³×C₄	D₄×C₁₃	1	8	yes	—
130	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
131	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
132	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
133	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
134	#117	—	2	32	no	—
135	C₂×C₄⋊C₄	—	2	4	no	—
136	C₂×C₄⋊C₄	—	2	4	no	—
137	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
138	C₂×C₂²⋊C₄	—	2	8	no	—
139	C₂×C₂²⋊C₄	—	2	8	no	—
140	C₂×C₂²⋊C₄	—	2	16	no	—
141	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
142	C₂×C₄²	—	2	8	no	—
143	C₂×C₄²	—	2	8	no	—
144	C₂×C₄²	—	2	16	no	—
145	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	—
146	#95	—	2	8	no	—
147	#95	—	2	32	no	—
148	C₂×C₁₃	—	4	4	no	—
149	C₂×C₁₃	C₂×#381	1	1	yes	characteristic
150	C₂×C₁₃	#2297	1	2	yes	—
151	C₂×C₁₃	#2298	1	4	yes	—
152	C₂×C₁₃	#2395	1	8	yes	—
153	C₂⁴	—	2	8	no	—
154	C₂⁴	—	2	4	no	—
155	C₂⁴	C₂²×C₄×C₁₃	1	2	yes	—
156	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
157	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
158	C₂²×C₄	—	2	4	no	—
159	C₂²×C₄	—	2	16	no	—
160	C₂²×C₄	—	2	32	no	—
161	C₂²×C₄	—	2	8	no	—
162	C₂²×C₄	—	2	4	no	—
163	C₂²×C₄	—	2	4	no	—
164	C₂²×C₄	—	2	16	no	—
165	C₂²×C₄	—	2	16	no	—
166	C₂²×C₄	—	2	16	no	—
167	C₂²×C₄	—	2	8	no	—
168	C₂²×C₄	C₁₃×C₂²⋊C₄	1	16	yes	—
169	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
170	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
171	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
172	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
173	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
174	C₂²×C₄	C₁₃×#41	1	16	yes	—
175	C₂²×C₄	C₁₃×#41	1	8	yes	—
176	C₄⋊C₄	—	2	16	no	—
177	C₂²⋊C₄	—	2	32	no	—
178	C₂²⋊C₄	—	2	16	no	—
179	C₄²	—	2	16	no	—
180	C₄²	—	4	16	no	—
181	C₁₃	#13853	1	1	yes	characteristic, direct product factor, Sylow
182	C₂³	—	2	4	no	—
183	C₂³	—	2	8	no	—
184	C₂³	—	2	8	no	—
185	C₂³	—	2	8	no	—
186	C₂³	—	2	8	no	—
187	C₂³	—	4	16	no	—
188	C₂³	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
189	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
190	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
191	C₂³	C₂×C₁₃×#41	1	4	yes	—
192	C₂³	C₂×C₁₃×#41	1	8	yes	—
193	C₂×C₄	—	2	4	no	—
194	C₂×C₄	—	2	8	no	—
195	C₂×C₄	—	2	32	no	—
196	C₂×C₄	—	2	8	no	—
197	C₂×C₄	—	2	16	no	—
198	C₂×C₄	—	2	16	no	—
199	C₂×C₄	—	2	32	no	—
200	C₂×C₄	—	4	8	no	—
201	C₂×C₄	—	4	8	no	—
202	C₂×C₄	—	4	16	no	—
203	C₂×C₄	—	4	8	no	—
204	C₂×C₄	—	4	8	no	—
205	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
206	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
207	C₂×C₄	C₁₃×#117	1	8	yes	—
208	C₂×C₄	C₁₃×#123	1	16	yes	—
209	C₂²	—	2	4	no	—
210	C₂²	—	2	8	no	—
211	C₂²	—	4	8	no	—
212	C₂²	—	4	16	no	—
213	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
214	C₂²	C₂×C₁₃×#117	1	2	yes	—
215	C₂²	C₄×C₁₃×#41	1	4	yes	—
216	C₂²	C₂×C₁₃×#123	1	4	yes	—
217	C₂²	C₁₃×#525	1	4	yes	—
218	C₂²	C₁₃×#529	1	16	yes	—
219	C₂²	C₁₃×#532	1	4	yes	—
220	C₄	—	2	4	no	—
221	C₄	—	4	8	no	—
222	C₄	—	4	16	no	—
223	C₄	C₁₃×#381	1	8	yes	—
224	C₂	—	4	4	no	—
225	C₂	C₂×C₁₃×#381	1	1	yes	characteristic
226	C₂	C₁₃×#2297	1	2	yes	—
227	C₂	C₁₃×#2298	1	4	yes	—
228	C₂	C₁₃×#2395	1	8	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₃	C₂³
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#1445	C₂	semidirect
5. C₄×C₁₃×#95	C₂	semidirect
8. C₂×C₁₃×#117	C₄	semidirect
39. #13853	C₁₃	direct (N × H)
70. #1445	C₂×C₁₃	semidirect
72. C₄×#95	C₂×C₁₃	semidirect
102. C₂×#117	C₄×C₁₃	semidirect
181. C₁₃	#13853	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×#117	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₁₃×#1445	2
C₁₃×#1440	2
C₄×C₁₃×#95	2
#13853	13

Subgroups — C13×#13853 #15700192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13853 #15700192