Subgroups — C₁₃×#14709 #15701048

Order 3328.

1662 conjugacy classes of subgroups.

The subgroup lattice has 242 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	1	yes	maximal, characteristic
2	C₂×C₁₃×#382	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1436	C₂	1	8	yes	maximal
5	C₁₃×C₄⋊#95	C₂	1	4	yes	maximal
6	C₂×C₁₃×#125	—	2	4	no	—
7	C₂×C₁₃×#125	—	2	4	no	—
8	C₂×C₁₃×#125	C₄	1	8	yes	complemented
9	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
12	C₂²×C₄²×C₁₃	C₂²	1	4	yes	—
13	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
14	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#382	—	2	4	no	—
16	C₂×C₁₃×#95	C₂²	1	4	yes	—
17	C₂×C₁₃×#95	C₂²	1	16	yes	—
18	C₄³×C₁₃	—	2	4	no	—
19	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
20	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
21	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
22	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
23	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₁₃×#125	—	2	32	no	—
25	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
28	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
31	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	16	yes	—
32	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
33	C₂×C₄²×C₁₃	—	2	8	no	—
34	C₂×C₄²×C₁₃	—	2	4	no	—
35	C₂×C₄²×C₁₃	—	2	16	no	—
36	C₂×C₄²×C₁₃	—	2	4	no	—
37	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
38	C₂×C₄²×C₁₃	D₄	1	4	yes	—
39	C₂×C₄²×C₁₃	D₄	1	4	yes	—
40	C₂×C₄²×C₁₃	Q₈	1	8	yes	—
41	C₁₃×#95	—	2	8	no	—
42	C₁₃×#95	—	2	32	no	—
43	#14709	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
45	C₂²×C₄×C₁₃	—	2	4	no	—
46	C₂²×C₄×C₁₃	—	2	8	no	—
47	C₂²×C₄×C₁₃	—	2	4	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	4	no	—
53	C₂²×C₄×C₁₃	—	2	16	no	—
54	C₂²×C₄×C₁₃	—	2	8	no	—
55	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
56	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
57	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
58	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
59	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
60	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
61	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
62	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
63	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
64	C₂²×C₄×C₁₃	#41	1	16	yes	—
65	C₂²×C₄×C₁₃	#41	1	4	yes	—
66	C₁₃×C₄⋊C₄	—	2	32	no	—
67	C₁₃×C₄⋊C₄	—	2	16	no	—
68	C₁₃×C₄⋊C₄	—	4	8	no	—
69	C₄²×C₁₃	—	2	32	no	—
70	C₄²×C₁₃	—	2	16	no	—
71	C₄²×C₁₃	C₂²⋊C₄	1	16	yes	—
72	C₂²×#125	C₂×C₁₃	1	1	yes	characteristic
73	C₂×#382	C₂×C₁₃	1	1	yes	characteristic
74	C₂×C₄³	C₂×C₁₃	1	1	yes	characteristic
75	#1436	C₂×C₁₃	1	8	yes	—
76	C₄⋊#95	C₂×C₁₃	1	4	yes	—
77	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
78	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
79	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
80	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
81	C₂³×C₁₃	C₂×#41	1	2	yes	—
82	C₂³×C₁₃	C₂×#41	1	8	yes	—
83	C₂×C₄×C₁₃	—	2	8	no	—
84	C₂×C₄×C₁₃	—	2	8	no	—
85	C₂×C₄×C₁₃	—	2	8	no	—
86	C₂×C₄×C₁₃	—	2	16	no	—
87	C₂×C₄×C₁₃	—	2	16	no	—
88	C₂×C₄×C₁₃	—	2	8	no	—
89	C₂×C₄×C₁₃	—	2	8	no	—
90	C₂×C₄×C₁₃	—	2	8	no	—
91	C₂×C₄×C₁₃	—	2	16	no	—
92	C₂×C₄×C₁₃	—	4	8	no	—
93	C₂×C₄×C₁₃	—	4	8	no	—
94	C₂×C₄×C₁₃	—	4	4	no	—
95	C₂×C₄×C₁₃	—	4	16	no	—
96	C₂×C₄×C₁₃	—	4	8	no	—
97	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	8	yes	—
98	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
99	C₂×C₄×C₁₃	C₄×Q₈	1	8	yes	—
100	C₂×C₄×C₁₃	C₂²⋊Q₈	1	8	yes	—
101	C₂×C₄×C₁₃	#124	1	4	yes	—
102	C₂×C₄×C₁₃	#125	1	16	yes	complemented
103	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
104	C₂×#125	—	2	4	no	—
105	C₂×#125	—	2	4	no	—
106	C₂×#125	C₄×C₁₃	1	8	yes	complemented
107	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
108	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
109	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
110	C₂²×C₄²	C₂²×C₁₃	1	4	yes	—
111	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
112	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
113	#382	—	2	4	no	—
114	C₂×#95	C₂²×C₁₃	1	16	yes	—
115	C₂×#95	C₂²×C₁₃	1	4	yes	—
116	C₄³	—	2	4	no	—
117	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₁₃	C₂×C₄×Q₈	1	2	yes	—
119	C₂²×C₁₃	C₄×#41	1	4	yes	—
120	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
121	C₂²×C₁₃	#525	1	4	yes	—
122	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
123	C₂²×C₁₃	C₂×#125	1	4	yes	—
124	C₂²×C₁₃	#529	1	8	yes	—
125	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
126	C₂²×C₁₃	#532	1	4	yes	—
127	C₂²×C₁₃	#533	1	4	yes	—
128	C₄×C₁₃	—	2	16	no	—
129	C₄×C₁₃	—	2	8	no	—
130	C₄×C₁₃	—	4	8	no	—
131	C₄×C₁₃	—	8	4	no	—
132	C₄×C₁₃	#391	1	8	yes	—
133	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
134	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
135	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
136	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
137	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
138	#125	—	2	32	no	—
139	C₂×C₄⋊C₄	—	2	8	no	—
140	C₂×C₄⋊C₄	—	2	8	no	—
141	C₂×C₄⋊C₄	—	2	4	no	—
142	C₂×C₄⋊C₄	—	2	4	no	—
143	C₂×C₄⋊C₄	—	2	4	no	—
144	C₂×C₄⋊C₄	—	2	8	no	—
145	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	16	yes	—
146	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
147	C₂×C₄²	—	2	8	no	—
148	C₂×C₄²	—	2	4	no	—
149	C₂×C₄²	—	2	16	no	—
150	C₂×C₄²	—	2	4	no	—
151	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
152	C₂×C₄²	D₄×C₁₃	1	4	yes	—
153	C₂×C₄²	D₄×C₁₃	1	4	yes	—
154	C₂×C₄²	Q₈×C₁₃	1	8	yes	—
155	#95	—	2	8	no	—
156	#95	—	2	32	no	—
157	C₂×C₁₃	C₂×#391	1	1	yes	characteristic
158	C₂×C₁₃	#2297	1	2	yes	—
159	C₂×C₁₃	C₄×#125	1	4	yes	—
160	C₂×C₁₃	#2851	1	4	yes	—
161	C₂×C₁₃	#2859	1	2	yes	—
162	C₂×C₁₃	#2861	1	2	yes	—
163	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
164	C₂²×C₄	—	2	4	no	—
165	C₂²×C₄	—	2	8	no	—
166	C₂²×C₄	—	2	4	no	—
167	C₂²×C₄	—	2	8	no	—
168	C₂²×C₄	—	2	4	no	—
169	C₂²×C₄	—	2	4	no	—
170	C₂²×C₄	—	2	16	no	—
171	C₂²×C₄	—	2	4	no	—
172	C₂²×C₄	—	2	16	no	—
173	C₂²×C₄	—	2	8	no	—
174	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
175	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
176	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
177	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
178	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
179	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
180	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
181	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
182	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
183	C₂²×C₄	C₁₃×#41	1	16	yes	—
184	C₂²×C₄	C₁₃×#41	1	4	yes	—
185	C₄⋊C₄	—	2	32	no	—
186	C₄⋊C₄	—	2	16	no	—
187	C₄⋊C₄	—	4	8	no	—
188	C₄²	—	2	32	no	—
189	C₄²	—	2	16	no	—
190	C₄²	C₁₃×C₂²⋊C₄	1	16	yes	—
191	C₁₃	#14709	1	1	yes	characteristic, direct product factor, Sylow
192	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
193	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
194	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
195	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
196	C₂³	C₂×C₁₃×#41	1	2	yes	—
197	C₂³	C₂×C₁₃×#41	1	8	yes	—
198	C₂×C₄	—	2	8	no	—
199	C₂×C₄	—	2	8	no	—
200	C₂×C₄	—	2	8	no	—
201	C₂×C₄	—	2	16	no	—
202	C₂×C₄	—	2	16	no	—
203	C₂×C₄	—	2	8	no	—
204	C₂×C₄	—	2	8	no	—
205	C₂×C₄	—	2	8	no	—
206	C₂×C₄	—	2	16	no	—
207	C₂×C₄	—	4	8	no	—
208	C₂×C₄	—	4	8	no	—
209	C₂×C₄	—	4	4	no	—
210	C₂×C₄	—	4	16	no	—
211	C₂×C₄	—	4	8	no	—
212	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	8	yes	—
213	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
214	C₂×C₄	C₄×Q₈×C₁₃	1	8	yes	—
215	C₂×C₄	C₁₃×C₂²⋊Q₈	1	8	yes	—
216	C₂×C₄	C₁₃×#124	1	4	yes	—
217	C₂×C₄	C₁₃×#125	1	16	yes	complemented
218	C₂×C₄	C₁₃×C₄⋊Q₈	1	4	yes	—
219	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
220	C₂²	C₂×C₄×Q₈×C₁₃	1	2	yes	—
221	C₂²	C₄×C₁₃×#41	1	4	yes	—
222	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	2	yes	—
223	C₂²	C₁₃×#525	1	4	yes	—
224	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
225	C₂²	C₂×C₁₃×#125	1	4	yes	—
226	C₂²	C₁₃×#529	1	8	yes	—
227	C₂²	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
228	C₂²	C₁₃×#532	1	4	yes	—
229	C₂²	C₁₃×#533	1	4	yes	—
230	C₄	—	2	8	no	—
231	C₄	—	2	16	no	—
232	C₄	—	4	8	no	—
233	C₄	—	8	4	no	—
234	C₄	C₁₃×#391	1	8	yes	—
235	C₂	C₂×C₁₃×#391	1	1	yes	characteristic
236	C₂	C₁₃×#2297	1	2	yes	—
237	C₂	C₄×C₁₃×#125	1	4	yes	—
238	C₂	C₁₃×#2851	1	4	yes	—
239	C₂	C₁₃×#2859	1	2	yes	—
240	C₂	C₁₃×#2861	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂⁴	C₂⁴×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
8. C₂×C₁₃×#125	C₄	semidirect
43. #14709	C₁₃	direct (N × H)
102. C₂×C₄×C₁₃	#125	semidirect
106. C₂×#125	C₄×C₁₃	semidirect
191. C₁₃	#14709	direct (N × H)
217. C₂×C₄	C₁₃×#125	semidirect

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
C₂×C₁₃×#382	2
C₂×C₄³×C₁₃	2
C₁₃×#1436	2
C₁₃×C₄⋊#95	2
#14709	13

Subgroups — C13×#14709 #15701048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#14709 #15701048