Subgroups — #15752399

Order 3328.

574 conjugacy classes of subgroups.

The subgroup lattice has 262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718587	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718586	C₂	1	1	yes	maximal, characteristic
3	#13112671	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
6	C₁₃×#431	—	2	2	no	—
7	C₁₃×#431	—	2	2	no	—
8	C₂×C₁₃×C₄⋊C₈	C₄	1	2	yes	—
9	C₂×C₁₃×C₂²⋊C₈	C₄	1	2	yes	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
11	C₂×C₂²⋊#1055	—	2	1	no	—
12	C₂×C₂²⋊#1055	—	2	1	no	—
13	#11718587	—	2	2	no	—
14	#11718587	C₄	1	4	yes	—
15	#11718586	—	2	2	no	—
16	#11718586	C₄	1	4	yes	—
17	C₂×C₄⋊#1055	C₂²	1	2	yes	—
18	C₂×C₄⋊#1055	C₂²	1	2	yes	—
19	C₂×#88043	—	2	1	no	—
20	C₂×C₄×#1055	—	2	1	no	—
21	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₃	Q₈	1	1	yes	characteristic
24	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
25	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₃	D₄	1	2	yes	—
30	C₂×C₄²×C₁₃	D₄	1	2	yes	—
31	C₂×C₄²×C₁₃	Q₈	1	1	yes	characteristic
32	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
33	C₂²×#1055	—	2	2	no	—
34	C₂²×#1055	—	2	2	no	—
35	C₁₃×C₄⋊C₈	—	2	4	no	—
36	C₁₃×C₂²⋊C₈	—	2	4	no	—
37	C₄×C₈×C₁₃	—	2	2	no	—
38	C₄×C₈×C₁₃	—	2	2	no	—
39	C₂²⋊#1055	—	2	4	no	—
40	C₂²⋊#1055	—	2	4	no	—
41	C₄⋊#1055	—	2	2	no	—
42	C₄⋊#1055	—	2	2	no	—
43	C₄⋊#1055	C₂×C₄	1	4	yes	—
44	C₄⋊#1055	C₂×C₄	1	4	yes	—
45	#88043	—	2	4	no	—
46	C₄×#1055	—	2	4	no	—
47	#7878	—	13	1	no	maximal, Sylow
48	C₂⁴×C₁₃	C₄⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	—	2	4	no	—
50	C₂²×C₄×C₁₃	—	2	4	no	—
51	C₂²×C₄×C₁₃	—	4	2	no	—
52	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
53	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
54	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
57	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
58	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
64	C₂×C₈×C₁₃	—	2	4	no	—
65	C₂×C₈×C₁₃	—	2	8	no	—
66	C₄²×C₁₃	C₄²	1	2	yes	—
67	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
68	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
69	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
70	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
71	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
72	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
73	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
74	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
76	C₂×#1055	—	2	4	no	—
77	C₂×#1055	—	2	4	no	—
78	C₂×#1055	—	4	4	no	—
79	C₂×#1055	—	4	4	no	—
80	C₂×#432	—	13	1	no	—
81	C₂×#431	—	13	1	no	—
82	C₂×#431	D₁₃	1	1	yes	characteristic
83	#1277	—	13	4	no	—
84	C₂³×C₁₃	—	2	2	no	—
85	C₂³×C₁₃	—	2	2	no	—
86	C₂³×C₁₃	—	2	2	no	—
87	C₂³×C₁₃	#95	1	2	yes	—
88	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₁₃	—	2	2	no	—
90	C₂×C₄×C₁₃	—	2	2	no	—
91	C₂×C₄×C₁₃	—	2	2	no	—
92	C₂×C₄×C₁₃	—	2	2	no	—
93	C₂×C₄×C₁₃	—	2	4	no	—
94	C₂×C₄×C₁₃	—	2	4	no	—
95	C₂×C₄×C₁₃	—	2	4	no	—
96	C₂×C₄×C₁₃	—	2	4	no	—
97	C₂×C₄×C₁₃	—	4	2	no	—
98	C₂×C₄×C₁₃	—	4	2	no	—
99	C₂×C₄×C₁₃	#95	1	2	yes	—
100	C₂×C₄×C₁₃	#95	1	2	yes	—
101	C₂×C₄×C₁₃	#95	1	2	yes	—
102	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
103	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×C₁₃	#131	1	4	yes	—
109	C₂×C₄×C₁₃	#135	1	4	yes	—
110	C₈×C₁₃	—	4	4	no	—
111	#1055	—	4	4	no	—
112	#1055	—	4	4	no	—
113	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
114	#432	—	13	4	no	—
115	#432	—	26	2	no	—
116	#431	—	2	2	no	—
117	#431	—	2	2	no	—
118	#431	—	13	4	no	—
119	#431	—	26	2	no	—
120	C₂×C₄⋊C₈	—	13	2	no	—
121	C₂×C₄⋊C₈	—	13	2	no	—
122	C₂×C₄⋊C₈	Dic₁₃	1	2	yes	—
123	C₂×C₂²⋊C₈	—	26	1	no	—
124	C₂×C₂²⋊C₈	—	26	1	no	—
125	C₂×C₂²⋊C₈	Dic₁₃	1	2	yes	—
126	C₂×#97	—	26	1	no	—
127	C₂×C₄×C₈	—	26	1	no	—
128	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
129	C₂²×C₁₃	—	2	2	no	—
130	C₂²×C₁₃	—	2	2	no	—
131	C₂²×C₁₃	—	2	2	no	—
132	C₂²×C₁₃	—	4	4	no	—
133	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
134	C₂²×C₁₃	#424	1	2	yes	—
135	C₂²×C₁₃	#427	1	2	yes	—
136	C₂²×C₁₃	#430	1	2	yes	—
137	C₄×C₁₃	—	2	2	no	—
138	C₄×C₁₃	—	2	2	no	—
139	C₄×C₁₃	—	2	2	no	—
140	C₄×C₁₃	—	2	1	no	—
141	C₄×C₁₃	—	2	1	no	—
142	C₄×C₁₃	#405	1	2	yes	—
143	C₄×C₁₃	#408	1	2	yes	—
144	C₄×C₁₃	#416	1	2	yes	—
145	C₄×C₁₃	#416	1	2	yes	—
146	C₂³×C₄	Dic₂₆	1	1	yes	characteristic
147	C₂³×C₄	D₅₂	1	1	yes	characteristic
148	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
149	C₂²×C₈	—	26	2	no	—
150	C₂²×C₈	—	26	2	no	—
151	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
152	C₂×C₄²	Dic₂₆	1	1	yes	characteristic
153	C₂×C₄²	C₄×D₁₃	1	2	yes	—
154	C₂×C₄²	C₄×D₁₃	1	2	yes	—
155	C₂×C₄²	D₅₂	1	1	yes	characteristic
156	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
157	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
158	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
159	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
160	C₄⋊C₈	—	2	4	no	—
161	C₄⋊C₈	—	13	4	no	—
162	C₄⋊C₈	—	13	4	no	—
163	C₄⋊C₈	—	26	2	no	—
164	C₄⋊C₈	—	26	2	no	—
165	C₂²⋊C₈	—	2	4	no	—
166	C₂²⋊C₈	—	26	4	no	—
167	C₂²⋊C₈	—	26	4	no	—
168	#97	—	26	4	no	—
169	C₄×C₈	—	2	2	no	—
170	C₄×C₈	—	2	2	no	—
171	C₄×C₈	—	26	4	no	—
172	C₂×C₁₃	—	4	2	no	—
173	C₂×C₁₃	#1572	1	4	yes	—
174	C₂×C₁₃	#1729	1	1	yes	characteristic
175	C₂×C₁₃	#1735	1	1	yes	characteristic
176	C₂×C₁₃	#1738	1	1	yes	characteristic
177	C₂⁴	C₄⋊Dic₁₃	1	1	yes	characteristic
178	C₂²×C₄	—	2	4	no	—
179	C₂²×C₄	—	2	4	no	—
180	C₂²×C₄	—	4	2	no	—
181	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
182	C₂²×C₄	#6101	1	2	yes	—
183	C₂²×C₄	#6101	1	2	yes	—
184	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
185	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
186	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
187	C₂²×C₄	#6103	1	2	yes	—
188	C₂²×C₄	#6103	1	2	yes	—
189	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
190	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
191	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
192	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
193	C₂×C₈	—	2	8	no	—
194	C₂×C₈	—	2	4	no	—
195	C₂×C₈	—	26	4	no	—
196	C₂×C₈	—	26	4	no	—
197	C₂×C₈	—	52	4	no	—
198	C₂×C₈	—	52	4	no	—
199	C₄²	C₄×Dic₁₃	1	2	yes	—
200	C₄²	#6101	1	2	yes	—
201	C₄²	#6101	1	2	yes	—
202	C₄²	#6103	1	2	yes	—
203	C₄²	#6103	1	2	yes	—
204	C₄²	C₂²⋊Dic₁₃	1	2	yes	—
205	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
206	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
207	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
208	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
209	C₁₃	#7878	1	1	yes	characteristic, complemented, Sylow
210	C₂³	—	2	2	no	—
211	C₂³	—	2	2	no	—
212	C₂³	—	2	2	no	—
213	C₂³	#88071	1	2	yes	—
214	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	2	4	no	—
220	C₂×C₄	—	2	4	no	—
221	C₂×C₄	—	2	4	no	—
222	C₂×C₄	—	2	4	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	#88071	1	2	yes	—
226	C₂×C₄	#88071	1	2	yes	—
227	C₂×C₄	#88071	1	2	yes	—
228	C₂×C₄	#88158	1	4	yes	—
229	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
230	C₂×C₄	C₂×#6101	1	1	yes	characteristic
231	C₂×C₄	C₂×#6101	1	1	yes	characteristic
232	C₂×C₄	C₂×#6103	1	1	yes	characteristic
233	C₂×C₄	C₂×#6103	1	1	yes	characteristic
234	C₂×C₄	#88202	1	4	yes	—
235	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
236	C₈	—	4	4	no	—
237	C₈	—	52	4	no	—
238	C₈	—	52	4	no	—
239	C₂²	—	2	2	no	—
240	C₂²	—	2	2	no	—
241	C₂²	—	2	2	no	—
242	C₂²	—	4	4	no	—
243	C₂²	#11718660	1	2	yes	—
244	C₂²	#11718767	1	2	yes	—
245	C₂²	#11718786	1	2	yes	—
246	C₂²	C₂×#88071	1	1	yes	characteristic
247	C₄	—	2	2	no	—
248	C₄	—	2	2	no	—
249	C₄	—	2	2	no	—
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	#11718658	1	2	yes	—
253	C₄	#11718774	1	2	yes	—
254	C₄	#11718774	1	2	yes	—
255	C₄	#11718895	1	2	yes	—
256	C₂	—	4	2	no	—
257	C₂	#13113616	1	4	yes	—
258	C₂	#13114533	1	1	yes	characteristic
259	C₂	#13114553	1	1	yes	characteristic
260	C₂	#13114563	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₂×C₁₃×#431	C₂
socle	C₂³×C₁₃	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₃	C₄⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₂×#431	D₁₃
hypocenter	C₁₃	#7878
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #13112671	C₂	semidirect
209. C₁₃	#7878	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718587	2
C₂×#11718586	2
#13112671	2
C₂×C₁₃×#431	2
#7878	13