Subgroups — #15850625

Order 3328.

706 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125423	C₂	1	2	yes	maximal
2	#13125420	C₂	1	2	yes	maximal
3	#13125347	C₂	1	2	yes	maximal
4	#13114454	C₂	1	1	yes	maximal, characteristic, complemented
5	#13114445	C₂	1	2	yes	maximal, complemented
6	#13114434	C₂	1	2	yes	maximal, complemented
7	#13114430	C₂	1	2	yes	maximal, complemented
8	C₈²×D₁₃	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1713	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719433	C₂²	1	4	yes	—
11	C₁₃×#500	C₂²	1	2	yes	—
12	C₁₃×#500	C₂²	1	2	yes	—
13	C₁₃×#494	C₂²	1	2	yes	—
14	#11718849	—	2	4	no	—
15	Q₁₆×Dic₁₃	—	2	4	no	—
16	#11718754	C₂²	1	4	yes	—
17	#11718742	C₂²	1	4	yes	—
18	#11718740	C₂²	1	4	yes	—
19	#11718548	—	2	4	no	—
20	#11718541	—	2	4	no	—
21	#11718539	—	2	4	no	—
22	#11718534	—	2	4	no	—
23	#11718360	C₂²	1	2	yes	—
24	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
25	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
26	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
27	#11718343	C₂²	1	2	yes	—
28	#11718343	C₂²	1	2	yes	—
29	C₈²×C₁₃	C₂²	1	1	yes	characteristic
30	C₈×#1055	C₂²	1	1	yes	characteristic
31	C₈×#1055	C₂²	1	1	yes	characteristic
32	C₈×#1055	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×Q₁₆	—	2	4	no	—
34	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
35	#88200	—	2	4	no	—
36	Q₈×Dic₁₃	—	2	4	no	—
37	C₂×Dic₅₂	—	2	4	no	—
38	C₂×C₈×D₁₃	D₄	1	2	yes	—
39	C₂×C₈×D₁₃	D₄	1	2	yes	—
40	C₂×C₈×D₁₃	D₄	1	2	yes	—
41	#88151	—	2	4	no	—
42	#88146	—	2	4	no	—
43	#88144	—	2	4	no	—
44	#88141	—	2	4	no	—
45	C₄²×D₁₃	C₂³	1	1	yes	characteristic
46	#88123	C₂³	1	4	yes	—
47	C₁₃×#107	—	2	4	no	—
48	C₁₃×#107	—	2	4	no	—
49	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	#88075	—	2	8	no	—
53	#88058	—	2	4	no	—
54	#88058	—	2	4	no	—
55	C₈×Dic₁₃	D₄	1	2	yes	—
56	C₈×Dic₁₃	D₄	1	2	yes	—
57	C₈×Dic₁₃	D₄	1	2	yes	—
58	#88050	—	2	8	no	—
59	#88048	—	2	8	no	—
60	C₄×#1055	C₂³	1	1	yes	characteristic
61	C₄×#1055	C₂³	1	1	yes	characteristic
62	C₄×#1055	C₂³	1	1	yes	characteristic
63	#19604	—	13	1	no	maximal, Sylow
64	C₂×Q₈×C₁₃	—	2	4	no	—
65	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
66	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
67	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
68	C₂×Dic₂₆	—	2	4	no	—
69	C₁₃×Q₁₆	—	4	8	no	—
70	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
71	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
72	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
73	C₁₃×C₄⋊C₄	—	2	4	no	—
74	C₁₃×C₄⋊C₄	—	2	4	no	—
75	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
76	#6103	—	4	4	no	—
77	C₄⋊Dic₁₃	—	2	4	no	—
78	C₄⋊Dic₁₃	—	2	4	no	—
79	C₄⋊Dic₁₃	—	4	4	no	—
80	#6101	—	4	4	no	—
81	C₄×Dic₁₃	—	4	4	no	—
82	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
83	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
84	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
85	C₂×#1055	C₂×D₄	1	2	yes	—
86	C₂×#1055	C₂×D₄	1	2	yes	—
87	C₂×#1055	C₂×D₄	1	2	yes	—
88	Dic₅₂	—	4	8	no	—
89	C₈×D₁₃	—	2	4	no	—
90	C₈×D₁₃	—	2	4	no	—
91	C₈×D₁₃	Q₁₆	1	8	yes	complemented
92	#3170	—	13	2	no	—
93	#3170	—	13	2	no	—
94	#3160	—	13	2	no	—
95	#1713	—	13	1	no	—
96	#1713	D₁₃	1	1	yes	characteristic, complemented
97	#1710	—	13	2	no	—
98	#1707	—	13	2	no	—
99	#1707	—	13	2	no	—
100	C₂×C₈²	—	13	1	no	—
101	C₂²×D₁₃	#127	1	1	yes	characteristic
102	Q₈×C₁₃	—	4	8	no	—
103	C₂×C₄×C₁₃	—	4	4	no	—
104	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
105	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
106	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
107	C₂×Dic₁₃	—	4	4	no	—
108	C₂×Dic₁₃	#127	1	1	yes	characteristic
109	C₂×Dic₁₃	#127	1	1	yes	characteristic
110	C₂×Dic₁₃	#127	1	1	yes	characteristic
111	C₄×D₁₃	—	2	2	no	—
112	C₄×D₁₃	—	2	2	no	—
113	C₄×D₁₃	C₂×Q₁₆	1	4	yes	—
114	Dic₂₆	—	4	8	no	—
115	C₈×C₁₃	C₂×Q₁₆	1	4	yes	—
116	C₈×C₁₃	#135	1	4	yes	—
117	C₈×C₁₃	#135	1	4	yes	—
118	#1055	—	2	2	no	—
119	#1055	—	2	2	no	—
120	#1055	C₂×Q₁₆	1	4	yes	—
121	#533	—	13	4	no	—
122	#500	—	13	2	no	—
123	#500	—	13	2	no	—
124	#500	C₂×D₁₃	1	2	yes	—
125	#500	C₂×D₁₃	1	2	yes	—
126	#499	—	26	4	no	—
127	#498	—	13	4	no	—
128	#494	—	13	2	no	—
129	#494	C₂×D₁₃	1	2	yes	—
130	#487	—	13	4	no	—
131	#487	—	13	4	no	—
132	#467	—	26	4	no	—
133	#467	—	26	4	no	—
134	C₄×Q₁₆	—	26	4	no	—
135	C₄×Q₁₆	—	26	4	no	—
136	#427	—	26	4	no	—
137	C₂×C₄×C₈	—	13	1	no	—
138	C₂×C₄×C₈	—	13	1	no	—
139	C₂×C₄×C₈	—	13	1	no	—
140	C₈²	—	13	1	no	—
141	C₈²	—	13	1	no	—
142	C₈²	—	13	1	no	—
143	C₈²	C₂×D₁₃	1	1	yes	characteristic
144	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
145	C₂×D₁₃	—	2	1	no	—
146	C₂×D₁₃	—	2	1	no	—
147	C₂×D₁₃	#494	1	2	yes	—
148	C₄×C₁₃	—	8	4	no	—
149	C₄×C₁₃	C₂²×Q₁₆	1	2	yes	—
150	C₄×C₁₃	C₂×#135	1	2	yes	—
151	C₄×C₁₃	C₂×#135	1	2	yes	—
152	Dic₁₃	—	2	1	no	—
153	Dic₁₃	—	2	1	no	—
154	Dic₁₃	—	8	4	no	—
155	Dic₁₃	#494	1	2	yes	—
156	C₂×Q₁₆	—	2	4	no	—
157	C₂×Q₁₆	—	26	4	no	—
158	C₂²×C₈	—	13	2	no	—
159	C₂²×C₈	—	13	2	no	—
160	C₂²×C₈	—	13	2	no	—
161	C₄⋊Q₈	—	13	4	no	—
162	C₄⋊Q₈	C₂²×D₁₃	1	4	yes	—
163	#125	—	26	4	no	—
164	C₂²⋊Q₈	—	26	4	no	—
165	C₂²⋊Q₈	—	26	4	no	—
166	C₄×Q₈	—	26	4	no	—
167	C₄×Q₈	—	26	4	no	—
168	#117	—	26	4	no	—
169	C₂×C₄²	—	13	1	no	—
170	#107	—	2	4	no	—
171	#107	—	2	4	no	—
172	#107	—	26	4	no	—
173	#107	—	26	4	no	—
174	#106	—	26	8	no	—
175	#103	—	26	8	no	—
176	#103	—	26	8	no	—
177	C₄×C₈	—	13	2	no	—
178	C₄×C₈	—	13	2	no	—
179	C₄×C₈	—	13	2	no	—
180	C₄×C₈	—	13	1	no	—
181	C₄×C₈	—	13	1	no	—
182	C₄×C₈	—	13	1	no	—
183	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
184	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
185	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
186	C₂×C₁₃	C₂×#494	1	1	yes	characteristic
187	C₂×C₁₃	#3147	1	1	yes	characteristic
188	C₂×C₁₃	#3147	1	1	yes	characteristic
189	D₁₃	—	2	2	no	—
190	C₂×Q₈	—	2	4	no	—
191	C₂×Q₈	—	26	4	no	—
192	C₂²×C₄	—	13	1	no	—
193	C₂²×C₄	—	13	1	no	—
194	C₂²×C₄	—	13	1	no	—
195	Q₁₆	—	4	8	no	—
196	Q₁₆	—	52	8	no	—
197	C₂×C₈	—	13	2	no	—
198	C₂×C₈	—	13	8	no	—
199	C₂×C₈	—	13	2	no	—
200	C₂×C₈	—	13	2	no	—
201	C₂×C₈	—	26	4	no	—
202	C₂×C₈	—	26	4	no	—
203	C₂×C₈	D₄×D₁₃	1	2	yes	—
204	C₂×C₈	D₄×D₁₃	1	2	yes	—
205	C₂×C₈	D₄×D₁₃	1	2	yes	—
206	C₄⋊C₄	—	2	4	no	—
207	C₄⋊C₄	—	2	4	no	—
208	C₄⋊C₄	—	26	4	no	—
209	C₄⋊C₄	—	26	4	no	—
210	C₄⋊C₄	—	52	4	no	—
211	C₄⋊C₄	—	52	4	no	—
212	C₂²⋊C₄	—	52	4	no	—
213	C₄²	—	13	1	no	—
214	C₄²	—	13	1	no	—
215	C₄²	—	13	1	no	—
216	C₄²	—	52	4	no	—
217	C₄²	C₂³×D₁₃	1	1	yes	characteristic
218	C₁₃	#19604	1	1	yes	characteristic, complemented, Sylow
219	C₂³	—	13	1	no	—
220	Q₈	—	4	8	no	—
221	Q₈	—	52	8	no	—
222	C₂×C₄	—	4	4	no	—
223	C₂×C₄	—	13	1	no	—
224	C₂×C₄	—	13	4	no	—
225	C₂×C₄	—	13	1	no	—
226	C₂×C₄	—	13	1	no	—
227	C₂×C₄	—	26	2	no	—
228	C₂×C₄	—	26	2	no	—
229	C₂×C₄	—	52	4	no	—
230	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
231	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
232	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
233	C₈	—	13	4	no	—
234	C₈	—	26	2	no	—
235	C₈	—	26	2	no	—
236	C₈	#88166	1	4	yes	—
237	C₈	Q₁₆×D₁₃	1	4	yes	—
238	C₈	#88173	1	4	yes	—
239	C₂²	—	13	2	no	—
240	C₂²	—	26	1	no	—
241	C₂²	—	26	1	no	—
242	C₂²	D₁₃×#127	1	1	yes	characteristic
243	C₄	—	8	4	no	—
244	C₄	—	13	2	no	—
245	C₄	—	26	1	no	—
246	C₄	—	26	1	no	—
247	C₄	—	104	4	no	—
248	C₄	C₂×#88166	1	2	yes	—
249	C₄	C₂×Q₁₆×D₁₃	1	2	yes	—
250	C₄	C₂×#88173	1	2	yes	—
251	C₂	—	26	2	no	—
252	C₂	D₁₃×#494	1	1	yes	characteristic
253	C₂	#13125263	1	1	yes	characteristic
254	C₂	#13125265	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₃×#127
commutator, cosocle	C₄²×C₁₃	C₂⁴
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1713	C₂
socle	C₂²×C₁₃	C₂×#127
prime radical	C₂²×D₁₃	#127
hypercenter	#1713	D₁₃
hypocenter	C₁₃	#19604
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1713

Complements

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

N	H ≅ G/N	type
4. #13114454	C₂	semidirect
5. #13114445	C₂	semidirect
6. #13114434	C₂	semidirect
7. #13114430	C₂	semidirect
9. C₁₃×#1713	C₂	semidirect
91. C₈×D₁₃	Q₁₆	semidirect
96. #1713	D₁₃	semidirect
218. C₁₃	#19604	semidirect

Maximal subgroups

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

subgroup	index
#13125423	2
#13125420	2
#13125347	2
#13114454	2
#13114445	2
#13114434	2
#13114430	2
C₈²×D₁₃	2
C₁₃×#1713	2
#19604	13