Subgroups — C₁₃×#14693 #15701032

Order 3328.

6494 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#385	C₂	1	6	yes	maximal, complemented
3	C₂×C₁₃×#379	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#379	C₂	1	1	yes	maximal, characteristic
5	C₁₃×C₂²⋊#95	C₂	1	6	yes	maximal, complemented
6	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
7	C₂⁴×C₄×C₁₃	—	2	4	no	—
8	C₂⁴×C₄×C₁₃	—	2	24	no	—
9	C₂⁴×C₄×C₁₃	C₂²	1	6	yes	—
10	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
11	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	3	yes	—
12	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	3	yes	—
13	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	6	yes	—
14	C₁₃×#385	—	2	24	no	—
15	C₁₃×#379	—	2	4	no	—
16	C₁₃×#379	C₄	1	8	yes	complemented
17	C₂×C₁₃×#95	C₂²	1	12	yes	complemented
18	C₂⁵×C₁₃	—	2	12	no	—
19	C₂⁵×C₁₃	—	2	12	no	—
20	C₂⁵×C₁₃	C₂×C₄	1	4	yes	—
21	C₂⁵×C₁₃	D₄	1	4	yes	—
22	C₂⁵×C₁₃	Q₈	1	4	yes	—
23	C₂⁵×C₁₃	C₂³	1	3	yes	—
24	C₂³×C₄×C₁₃	—	2	96	no	—
25	C₂³×C₄×C₁₃	—	2	128	no	—
26	C₂³×C₄×C₁₃	—	2	12	no	—
27	C₂³×C₄×C₁₃	—	2	12	no	—
28	C₂³×C₄×C₁₃	—	2	48	no	—
29	C₂³×C₄×C₁₃	D₄	1	24	yes	—
30	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
31	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
32	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
33	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
34	C₂×C₁₃×C₄⋊C₄	—	2	24	no	—
35	C₂×C₁₃×C₂²⋊C₄	—	2	12	no	—
36	C₂×C₁₃×C₂²⋊C₄	—	2	12	no	—
37	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
38	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
39	C₂×C₁₃×C₂²⋊C₄	—	2	12	no	—
40	C₂×C₁₃×C₂²⋊C₄	—	2	12	no	—
41	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	24	yes	complemented
42	C₁₃×#95	—	2	24	no	—
43	#14693	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂⁴×C₁₃	—	2	32	no	—
45	C₂⁴×C₁₃	—	2	96	no	—
46	C₂⁴×C₁₃	—	2	48	no	—
47	C₂⁴×C₁₃	—	2	24	no	—
48	C₂⁴×C₁₃	—	2	48	no	—
49	C₂⁴×C₁₃	—	2	24	no	—
50	C₂⁴×C₁₃	—	2	12	no	—
51	C₂⁴×C₁₃	—	2	12	no	—
52	C₂⁴×C₁₃	C₄⋊C₄	1	16	yes	complemented
53	C₂⁴×C₁₃	C₂²×C₄	1	6	yes	—
54	C₂⁴×C₁₃	C₂×D₄	1	6	yes	—
55	C₂⁴×C₁₃	C₂×D₄	1	12	yes	—
56	C₂⁴×C₁₃	C₂×Q₈	1	6	yes	—
57	C₂⁴×C₁₃	#41	1	12	yes	—
58	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
59	C₂²×C₄×C₁₃	—	2	256	no	—
60	C₂²×C₄×C₁₃	—	2	96	no	—
61	C₂²×C₄×C₁₃	—	2	96	no	—
62	C₂²×C₄×C₁₃	—	2	48	no	—
63	C₂²×C₄×C₁₃	—	2	4	no	—
64	C₂²×C₄×C₁₃	—	2	12	no	—
65	C₂²×C₄×C₁₃	—	2	96	no	—
66	C₂²×C₄×C₁₃	—	2	12	no	—
67	C₂²×C₄×C₁₃	—	2	12	no	—
68	C₂²×C₄×C₁₃	—	2	6	no	—
69	C₂²×C₄×C₁₃	—	2	1	no	—
70	C₂²×C₄×C₁₃	—	2	3	no	—
71	C₂²×C₄×C₁₃	—	2	6	no	—
72	C₂²×C₄×C₁₃	—	2	12	no	—
73	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	complemented
74	C₂²×C₄×C₁₃	C₂×D₄	1	24	yes	—
75	C₁₃×C₄⋊C₄	—	4	16	no	—
76	C₁₃×C₂²⋊C₄	—	2	48	no	—
77	C₁₃×C₂²⋊C₄	—	4	12	no	—
78	C₁₃×C₂²⋊C₄	—	4	12	no	—
79	C₂⁵×C₄	C₂×C₁₃	1	1	yes	characteristic
80	C₂×#385	C₂×C₁₃	1	6	yes	complemented
81	C₂×#379	C₂×C₁₃	1	1	yes	characteristic
82	C₂×#379	C₂×C₁₃	1	1	yes	characteristic
83	C₂²⋊#95	C₂×C₁₃	1	6	yes	complemented
84	C₂³×C₁₃	—	2	32	no	—
85	C₂³×C₁₃	—	2	128	no	—
86	C₂³×C₁₃	—	2	96	no	—
87	C₂³×C₁₃	—	2	128	no	—
88	C₂³×C₁₃	—	2	24	no	—
89	C₂³×C₁₃	—	2	24	no	—
90	C₂³×C₁₃	—	2	12	no	—
91	C₂³×C₁₃	—	2	24	no	—
92	C₂³×C₁₃	—	2	12	no	—
93	C₂³×C₁₃	—	2	24	no	—
94	C₂³×C₁₃	—	2	48	no	—
95	C₂³×C₁₃	—	2	96	no	—
96	C₂³×C₁₃	C₂×C₄⋊C₄	1	12	yes	—
97	C₂³×C₁₃	C₄×D₄	1	24	yes	—
98	C₂³×C₁₃	#120	1	12	yes	—
99	C₂³×C₁₃	C₂²⋊Q₈	1	24	yes	—
100	C₂³×C₁₃	#123	1	12	yes	—
101	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
102	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
103	C₂³×C₁₃	C₂²×D₄	1	6	yes	—
104	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
105	C₂³×C₁₃	C₂×#41	1	6	yes	—
106	C₂×C₄×C₁₃	—	2	192	no	—
107	C₂×C₄×C₁₃	—	2	24	no	—
108	C₂×C₄×C₁₃	—	2	24	no	—
109	C₂×C₄×C₁₃	—	2	24	no	—
110	C₂×C₄×C₁₃	—	4	4	no	—
111	C₂×C₄×C₁₃	—	4	12	no	—
112	C₂×C₄×C₁₃	—	4	3	no	—
113	C₂×C₄×C₁₃	—	4	3	no	—
114	C₂×C₄×C₁₃	—	4	4	no	—
115	C₂×C₄×C₁₃	—	4	6	no	—
116	C₂×C₄×C₁₃	—	4	12	no	—
117	C₂×C₄×C₁₃	#120	1	16	yes	—
118	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
119	C₂⁴×C₄	—	2	4	no	—
120	C₂⁴×C₄	—	2	24	no	—
121	C₂⁴×C₄	C₂²×C₁₃	1	6	yes	—
122	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
123	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	3	yes	—
124	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	3	yes	—
125	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	6	yes	—
126	#385	—	2	24	no	—
127	#379	—	2	4	no	—
128	#379	C₄×C₁₃	1	8	yes	complemented
129	C₂×#95	C₂²×C₁₃	1	12	yes	complemented
130	C₂²×C₁₃	—	2	128	no	—
131	C₂²×C₁₃	—	2	12	no	—
132	C₂²×C₁₃	—	2	48	no	—
133	C₂²×C₁₃	—	2	12	no	—
134	C₂²×C₁₃	—	2	24	no	—
135	C₂²×C₁₃	—	2	24	no	—
136	C₂²×C₁₃	—	2	48	no	—
137	C₂²×C₁₃	#385	1	24	yes	complemented
138	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
139	C₂²×C₁₃	C₂×C₄×D₄	1	6	yes	—
140	C₂²×C₁₃	C₂×#120	1	4	yes	—
141	C₂²×C₁₃	C₂×#120	1	3	yes	—
142	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	6	yes	—
143	C₂²×C₁₃	C₂×#123	1	3	yes	—
144	C₂²×C₁₃	#525	1	12	yes	—
145	C₄×C₁₃	—	2	16	no	—
146	C₄×C₁₃	—	4	8	no	—
147	C₄×C₁₃	—	8	1	no	—
148	C₄×C₁₃	—	8	3	no	—
149	C₂⁵	—	2	12	no	—
150	C₂⁵	—	2	12	no	—
151	C₂⁵	C₂×C₄×C₁₃	1	4	yes	—
152	C₂⁵	D₄×C₁₃	1	4	yes	—
153	C₂⁵	Q₈×C₁₃	1	4	yes	—
154	C₂⁵	C₂³×C₁₃	1	3	yes	—
155	C₂³×C₄	—	2	96	no	—
156	C₂³×C₄	—	2	128	no	—
157	C₂³×C₄	—	2	12	no	—
158	C₂³×C₄	—	2	12	no	—
159	C₂³×C₄	—	2	48	no	—
160	C₂³×C₄	D₄×C₁₃	1	24	yes	—
161	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
162	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
163	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
164	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
165	C₂×C₄⋊C₄	—	2	24	no	—
166	C₂×C₂²⋊C₄	—	2	12	no	—
167	C₂×C₂²⋊C₄	—	2	12	no	—
168	C₂×C₂²⋊C₄	—	2	6	no	—
169	C₂×C₂²⋊C₄	—	2	6	no	—
170	C₂×C₂²⋊C₄	—	2	12	no	—
171	C₂×C₂²⋊C₄	—	2	12	no	—
172	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	24	yes	complemented
173	#95	—	2	24	no	—
174	C₂×C₁₃	—	2	24	no	—
175	C₂×C₁₃	C₂×#385	1	3	yes	—
176	C₂×C₁₃	C₄×#120	1	4	yes	—
177	C₂×C₁₃	#2846	1	1	yes	characteristic
178	C₂×C₁₃	#2848	1	4	yes	—
179	C₂×C₁₃	#2849	1	3	yes	—
180	C₂⁴	—	2	32	no	—
181	C₂⁴	—	2	96	no	—
182	C₂⁴	—	2	48	no	—
183	C₂⁴	—	2	24	no	—
184	C₂⁴	—	2	48	no	—
185	C₂⁴	—	2	24	no	—
186	C₂⁴	—	2	12	no	—
187	C₂⁴	—	2	12	no	—
188	C₂⁴	C₁₃×C₄⋊C₄	1	16	yes	complemented
189	C₂⁴	C₂²×C₄×C₁₃	1	6	yes	—
190	C₂⁴	C₂×D₄×C₁₃	1	6	yes	—
191	C₂⁴	C₂×D₄×C₁₃	1	12	yes	—
192	C₂⁴	C₂×Q₈×C₁₃	1	6	yes	—
193	C₂⁴	C₁₃×#41	1	12	yes	—
194	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
195	C₂²×C₄	—	2	256	no	—
196	C₂²×C₄	—	2	96	no	—
197	C₂²×C₄	—	2	96	no	—
198	C₂²×C₄	—	2	48	no	—
199	C₂²×C₄	—	2	4	no	—
200	C₂²×C₄	—	2	12	no	—
201	C₂²×C₄	—	2	96	no	—
202	C₂²×C₄	—	2	12	no	—
203	C₂²×C₄	—	2	12	no	—
204	C₂²×C₄	—	2	6	no	—
205	C₂²×C₄	—	2	1	no	—
206	C₂²×C₄	—	2	3	no	—
207	C₂²×C₄	—	2	6	no	—
208	C₂²×C₄	—	2	12	no	—
209	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	complemented
210	C₂²×C₄	C₂×D₄×C₁₃	1	24	yes	—
211	C₄⋊C₄	—	4	16	no	—
212	C₂²⋊C₄	—	2	48	no	—
213	C₂²⋊C₄	—	4	12	no	—
214	C₂²⋊C₄	—	4	12	no	—
215	C₁₃	#14693	1	1	yes	characteristic, direct product factor, Sylow
216	C₂³	—	2	32	no	—
217	C₂³	—	2	128	no	—
218	C₂³	—	2	128	no	—
219	C₂³	—	2	96	no	—
220	C₂³	—	2	96	no	—
221	C₂³	—	2	24	no	—
222	C₂³	—	2	12	no	—
223	C₂³	—	2	24	no	—
224	C₂³	—	2	24	no	—
225	C₂³	—	2	12	no	—
226	C₂³	—	2	24	no	—
227	C₂³	—	2	48	no	—
228	C₂³	C₂×C₁₃×C₄⋊C₄	1	12	yes	—
229	C₂³	C₄×D₄×C₁₃	1	24	yes	—
230	C₂³	C₁₃×#120	1	12	yes	—
231	C₂³	C₁₃×C₂²⋊Q₈	1	24	yes	—
232	C₂³	C₁₃×#123	1	12	yes	—
233	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
234	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
235	C₂³	C₂²×D₄×C₁₃	1	6	yes	—
236	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
237	C₂³	C₂×C₁₃×#41	1	6	yes	—
238	C₂×C₄	—	2	192	no	—
239	C₂×C₄	—	2	24	no	—
240	C₂×C₄	—	2	24	no	—
241	C₂×C₄	—	2	24	no	—
242	C₂×C₄	—	4	4	no	—
243	C₂×C₄	—	4	12	no	—
244	C₂×C₄	—	4	3	no	—
245	C₂×C₄	—	4	3	no	—
246	C₂×C₄	—	4	4	no	—
247	C₂×C₄	—	4	6	no	—
248	C₂×C₄	—	4	12	no	—
249	C₂×C₄	C₁₃×#120	1	16	yes	—
250	C₂²	—	2	128	no	—
251	C₂²	—	2	24	no	—
252	C₂²	—	2	48	no	—
253	C₂²	—	2	12	no	—
254	C₂²	—	2	48	no	—
255	C₂²	—	2	12	no	—
256	C₂²	—	2	24	no	—
257	C₂²	C₁₃×#385	1	24	yes	complemented
258	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
259	C₂²	C₂×C₄×D₄×C₁₃	1	6	yes	—
260	C₂²	C₂×C₁₃×#120	1	3	yes	—
261	C₂²	C₂×C₁₃×#120	1	4	yes	—
262	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	6	yes	—
263	C₂²	C₂×C₁₃×#123	1	3	yes	—
264	C₂²	C₁₃×#525	1	12	yes	—
265	C₄	—	2	16	no	—
266	C₄	—	4	8	no	—
267	C₄	—	8	1	no	—
268	C₄	—	8	3	no	—
269	C₂	—	2	24	no	—
270	C₂	C₂×C₁₃×#385	1	3	yes	—
271	C₂	C₄×C₁₃×#120	1	4	yes	—
272	C₂	C₁₃×#2846	1	1	yes	characteristic
273	C₂	C₁₃×#2848	1	4	yes	—
274	C₂	C₁₃×#2849	1	3	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
prime radical	C₂⁶×C₁₃	C₂²
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. C₂×C₁₃×#385	C₂	semidirect
5. C₁₃×C₂²⋊#95	C₂	semidirect
10. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
16. C₁₃×#379	C₄	semidirect
17. C₂×C₁₃×#95	C₂²	semidirect
41. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
43. #14693	C₁₃	direct (N × H)
52. C₂⁴×C₁₃	C₄⋊C₄	semidirect
73. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
80. C₂×#385	C₂×C₁₃	semidirect
83. C₂²⋊#95	C₂×C₁₃	semidirect
122. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
128. #379	C₄×C₁₃	semidirect
129. C₂×#95	C₂²×C₁₃	semidirect
137. C₂²×C₁₃	#385	semidirect
172. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
188. C₂⁴	C₁₃×C₄⋊C₄	semidirect
209. C₂²×C₄	C₂²×C₄×C₁₃	semidirect
215. C₁₃	#14693	direct (N × H)
257. C₂²	C₁₃×#385	semidirect

Maximal subgroups

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

subgroup	index
C₂⁵×C₄×C₁₃	2
C₂×C₁₃×#385	2
C₂×C₁₃×#379	2
C₁₃×C₂²⋊#95	2
#14693	13

Subgroups — C13×#14693 #15701032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#14693 #15701032