Subgroups — #15779873

Order 3328.

530 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718767	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718156	C₂	1	2	yes	maximal, complemented
3	C₂×C₂²⋊#6090	C₂	1	1	yes	maximal, characteristic
4	#13112927	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
9	C₂×#88180	—	2	1	no	—
10	C₁₃×#467	—	2	2	no	—
11	C₁₃×#467	C₄	1	4	yes	complemented
12	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#103	—	2	1	no	—
14	#11718767	—	2	4	no	—
15	C₂×#88058	C₂²	1	2	yes	—
16	C₂×#88057	—	2	1	no	—
17	C₂²×#6090	C₂²	1	2	yes	—
18	#11718156	—	2	4	no	—
19	C₂²⋊#6090	—	2	2	no	—
20	C₂²×Q₈×C₁₃	—	2	1	no	—
21	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
22	C₂×C₁₃×Q₁₆	—	2	2	no	—
23	C₂×C₁₃×Q₁₆	—	2	1	no	—
24	C₂×C₁₃×Q₁₆	—	2	2	no	—
25	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
26	C₂²×C₈×C₁₃	—	2	2	no	—
27	C₂²×C₈×C₁₃	—	2	2	no	—
28	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
29	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₃	D₄	1	2	yes	—
31	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
32	C₁₃×C₂²⋊Q₈	—	2	4	no	—
33	C₁₃×C₂²⋊Q₈	—	4	2	no	—
34	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
35	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
36	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
37	C₂×C₂²⋊Dic₁₃	—	4	1	no	—
38	#88180	—	2	4	no	—
39	#88180	—	4	2	no	—
40	C₂×C₄⋊Dic₁₃	—	2	2	no	—
41	C₂×C₄×Dic₁₃	—	4	1	no	—
42	C₁₃×#107	—	2	1	no	—
43	C₁₃×#107	C₂×C₄	1	2	yes	—
44	C₁₃×#103	—	2	4	no	—
45	#88058	—	2	2	no	—
46	#88058	D₄	1	4	yes	—
47	#88057	—	2	4	no	—
48	C₂×#6090	—	2	2	no	—
49	C₂×#6090	—	2	2	no	—
50	C₂×#6090	—	2	2	no	—
51	#12994	—	13	1	no	maximal, Sylow
52	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
53	C₂×Q₈×C₁₃	—	2	2	no	—
54	C₂×Q₈×C₁₃	—	4	1	no	—
55	C₂×Q₈×C₁₃	—	4	1	no	—
56	C₂×Q₈×C₁₃	—	4	1	no	—
57	C₂×Q₈×C₁₃	—	4	1	no	—
58	C₂×Q₈×C₁₃	—	4	1	no	—
59	C₂²×C₄×C₁₃	—	2	1	no	—
60	C₂²×C₄×C₁₃	—	2	1	no	—
61	C₂²×C₄×C₁₃	—	2	1	no	—
62	C₂²×C₄×C₁₃	—	2	1	no	—
63	C₂²×C₄×C₁₃	—	4	1	no	—
64	C₂²×C₄×C₁₃	—	4	1	no	—
65	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
66	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
68	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
69	C₂²×Dic₁₃	—	4	2	no	—
70	C₁₃×Q₁₆	—	2	4	no	—
71	C₁₃×Q₁₆	—	4	2	no	—
72	C₂×C₈×C₁₃	—	2	1	no	—
73	C₂×C₈×C₁₃	—	2	1	no	—
74	C₂×C₈×C₁₃	—	2	4	no	—
75	C₂×C₈×C₁₃	—	2	4	no	—
76	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
77	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
79	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
80	C₂×C₈×C₁₃	#41	1	2	yes	—
81	C₁₃×C₄⋊C₄	—	2	2	no	—
82	C₁₃×C₄⋊C₄	—	4	4	no	—
83	C₁₃×C₄⋊C₄	—	4	1	no	—
84	C₁₃×C₂²⋊C₄	—	4	4	no	—
85	C₂²⋊Dic₁₃	—	4	4	no	—
86	C₄⋊Dic₁₃	—	2	4	no	—
87	C₄⋊Dic₁₃	—	4	2	no	—
88	C₄×Dic₁₃	—	4	4	no	—
89	#6090	—	4	2	no	—
90	C₂×#467	D₁₃	1	1	yes	characteristic
91	C₂×#427	—	13	1	no	—
92	C₂×#358	—	13	2	no	—
93	C₂×C₂²⋊C₁₆	—	13	1	no	—
94	#1380	—	13	2	no	—
95	C₂³×C₁₃	—	2	1	no	—
96	C₂³×C₁₃	—	2	1	no	—
97	C₂³×C₁₃	—	2	2	no	—
98	C₂³×C₁₃	—	2	2	no	—
99	C₂³×C₁₃	#102	1	2	yes	—
100	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
101	Q₈×C₁₃	—	4	2	no	—
102	Q₈×C₁₃	—	4	2	no	—
103	Q₈×C₁₃	—	8	1	no	—
104	Q₈×C₁₃	—	8	1	no	—
105	C₂×C₄×C₁₃	—	2	1	no	—
106	C₂×C₄×C₁₃	—	2	1	no	—
107	C₂×C₄×C₁₃	—	2	2	no	—
108	C₂×C₄×C₁₃	—	2	2	no	—
109	C₂×C₄×C₁₃	—	2	2	no	—
110	C₂×C₄×C₁₃	—	2	2	no	—
111	C₂×C₄×C₁₃	—	4	2	no	—
112	C₂×C₄×C₁₃	—	4	2	no	—
113	C₂×C₄×C₁₃	—	8	1	no	—
114	C₂×C₄×C₁₃	—	8	1	no	—
115	C₂×C₄×C₁₃	—	8	2	no	—
116	C₂×C₄×C₁₃	#102	1	2	yes	—
117	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
118	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
119	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
120	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
121	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
122	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
123	C₂×Dic₁₃	—	4	4	no	—
124	C₂×Dic₁₃	—	8	2	no	—
125	C₂×Dic₁₃	—	8	2	no	—
126	C₈×C₁₃	—	2	2	no	—
127	C₈×C₁₃	C₄×D₄	1	2	yes	—
128	C₈×C₁₃	#121	1	2	yes	—
129	C₂²×Q₁₆	C₂×D₁₃	1	1	yes	characteristic
130	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
131	C₂×C₂²⋊Q₈	—	2	1	no	—
132	C₂×#117	—	26	1	no	—
133	C₂²×C₁₆	—	13	2	no	—
134	#467	—	2	2	no	—
135	#467	Dic₁₃	1	4	yes	complemented
136	#427	—	26	4	no	—
137	C₂×#107	—	13	2	no	—
138	C₂×#107	C₂×D₁₃	1	1	yes	characteristic
139	C₂×#106	—	26	1	no	—
140	C₂×#103	—	2	1	no	—
141	#358	—	26	4	no	—
142	C₂²⋊C₁₆	—	26	2	no	—
143	C₂²×C₁₃	—	2	2	no	—
144	C₂²×C₁₃	—	2	2	no	—
145	C₂²×C₁₃	—	2	2	no	—
146	C₂²×C₁₃	—	4	2	no	—
147	C₂²×C₁₃	—	4	2	no	—
148	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
149	C₂²×C₁₃	#447	1	1	yes	characteristic
150	C₂²×C₁₃	#480	1	1	yes	characteristic
151	C₂²×C₁₃	#508	1	2	yes	—
152	C₂²×C₁₃	#510	1	2	yes	—
153	C₄×C₁₃	—	2	2	no	—
154	C₄×C₁₃	—	8	2	no	—
155	C₄×C₁₃	—	8	2	no	—
156	C₄×C₁₃	#386	1	1	yes	characteristic
157	C₄×C₁₃	#417	1	1	yes	characteristic
158	C₄×C₁₃	#448	1	1	yes	characteristic
159	C₄×C₁₃	#481	1	1	yes	characteristic
160	Dic₁₃	—	8	4	no	—
161	C₂²×Q₈	—	2	1	no	—
162	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
163	C₂×Q₁₆	—	2	2	no	—
164	C₂×Q₁₆	—	2	2	no	—
165	C₂×Q₁₆	—	2	1	no	—
166	C₂×Q₁₆	C₂×Dic₁₃	1	2	yes	—
167	C₂²×C₈	—	2	2	no	—
168	C₂²×C₈	—	2	2	no	—
169	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
170	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
171	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
172	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
173	C₂²⋊Q₈	—	2	4	no	—
174	C₂²⋊Q₈	—	4	2	no	—
175	#117	—	26	4	no	—
176	#117	—	52	2	no	—
177	C₂×C₄⋊C₄	—	2	1	no	—
178	C₂×C₄⋊C₄	—	4	1	no	—
179	C₂×C₄⋊C₄	—	26	2	no	—
180	C₂×C₂²⋊C₄	—	4	1	no	—
181	C₂×C₂²⋊C₄	—	52	1	no	—
182	C₂×C₄²	—	52	1	no	—
183	C₂×C₁₆	—	26	2	no	—
184	C₂×C₁₆	—	26	2	no	—
185	C₂×C₁₆	—	26	2	no	—
186	#107	—	2	1	no	—
187	#107	—	13	4	no	—
188	#107	—	26	2	no	—
189	#107	C₂×Dic₁₃	1	2	yes	—
190	#106	—	26	4	no	—
191	#103	—	2	4	no	—
192	C₂×C₁₃	—	4	2	no	—
193	C₂×C₁₃	#1874	1	1	yes	characteristic
194	C₂×C₁₃	#2138	1	1	yes	characteristic
195	C₂×C₁₃	#2141	1	1	yes	characteristic
196	C₂×C₁₃	#2189	1	2	yes	—
197	C₂×C₁₃	#2237	1	2	yes	—
198	C₂⁴	#6104	1	1	yes	characteristic
199	C₂×Q₈	—	2	2	no	—
200	C₂×Q₈	—	4	1	no	—
201	C₂×Q₈	—	4	1	no	—
202	C₂×Q₈	—	4	1	no	—
203	C₂×Q₈	—	4	1	no	—
204	C₂×Q₈	—	4	1	no	—
205	C₂²×C₄	—	2	1	no	—
206	C₂²×C₄	—	2	1	no	—
207	C₂²×C₄	—	2	1	no	—
208	C₂²×C₄	—	2	1	no	—
209	C₂²×C₄	—	4	1	no	—
210	C₂²×C₄	—	4	1	no	—
211	C₂²×C₄	—	52	2	no	—
212	C₂²×C₄	#6104	1	1	yes	characteristic
213	C₂²×C₄	#6105	1	2	yes	—
214	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
215	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
216	Q₁₆	—	2	4	no	—
217	Q₁₆	—	4	2	no	—
218	C₂×C₈	—	2	1	no	—
219	C₂×C₈	—	2	1	no	—
220	C₂×C₈	—	2	4	no	—
221	C₂×C₈	—	2	4	no	—
222	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
223	C₂×C₈	D₄×D₁₃	1	2	yes	—
224	C₂×C₈	#6129	1	2	yes	—
225	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
226	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
227	C₄⋊C₄	—	2	2	no	—
228	C₄⋊C₄	—	4	4	no	—
229	C₄⋊C₄	—	4	1	no	—
230	C₄⋊C₄	—	26	4	no	—
231	C₄⋊C₄	—	52	2	no	—
232	C₂²⋊C₄	—	4	4	no	—
233	C₂²⋊C₄	—	52	4	no	—
234	C₄²	—	52	4	no	—
235	C₁₆	—	52	2	no	—
236	C₁₃	#12994	1	1	yes	characteristic, complemented, Sylow
237	C₂³	—	2	1	no	—
238	C₂³	—	2	1	no	—
239	C₂³	—	2	2	no	—
240	C₂³	—	2	2	no	—
241	C₂³	#88072	1	2	yes	—
242	C₂³	C₂×#6104	1	1	yes	characteristic
243	Q₈	—	4	2	no	—
244	Q₈	—	4	2	no	—
245	Q₈	—	8	1	no	—
246	Q₈	—	8	1	no	—
247	C₂×C₄	—	2	1	no	—
248	C₂×C₄	—	2	1	no	—
249	C₂×C₄	—	2	2	no	—
250	C₂×C₄	—	2	2	no	—
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	4	2	no	—
254	C₂×C₄	—	4	2	no	—
255	C₂×C₄	—	8	1	no	—
256	C₂×C₄	—	8	1	no	—
257	C₂×C₄	—	8	2	no	—
258	C₂×C₄	—	52	4	no	—
259	C₂×C₄	—	104	2	no	—
260	C₂×C₄	—	104	2	no	—
261	C₂×C₄	#88072	1	2	yes	—
262	C₂×C₄	C₂×#6105	1	1	yes	characteristic
263	C₂×C₄	#88189	1	1	yes	characteristic
264	C₂×C₄	#88191	1	1	yes	characteristic
265	C₂×C₄	#88203	1	1	yes	characteristic
266	C₂×C₄	#88205	1	1	yes	characteristic
267	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
268	C₈	—	2	2	no	—
269	C₈	D₄×Dic₁₃	1	2	yes	—
270	C₈	#88193	1	2	yes	—
271	C₂²	—	2	2	no	—
272	C₂²	—	2	2	no	—
273	C₂²	—	2	2	no	—
274	C₂²	—	4	2	no	—
275	C₂²	—	4	2	no	—
276	C₂²	#11718694	1	1	yes	characteristic
277	C₂²	#11718697	1	1	yes	characteristic
278	C₂²	#11718840	1	2	yes	—
279	C₂²	#11718855	1	2	yes	—
280	C₂²	C₂×#88072	1	1	yes	characteristic
281	C₄	—	2	2	no	—
282	C₄	—	8	2	no	—
283	C₄	—	8	2	no	—
284	C₄	—	104	4	no	—
285	C₄	#11718695	1	1	yes	characteristic
286	C₄	#11718701	1	1	yes	characteristic
287	C₄	#11718881	1	1	yes	characteristic
288	C₄	#11718893	1	1	yes	characteristic
289	C₂	—	4	2	no	—
290	C₂	#13115154	1	1	yes	characteristic
291	C₂	#13116543	1	1	yes	characteristic
292	C₂	#13116556	1	1	yes	characteristic
293	C₂	#13116774	1	2	yes	—
294	C₂	#13117041	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×#6104
commutator	C₂×C₈×C₁₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×#467	C₂
socle	C₂³×C₁₃	C₂×D₈
prime radical	C₂⁴×C₁₃	D₈
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×#467	D₁₃
hypocenter	C₁₃	#12994
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂×#467

Complements

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

N	H ≅ G/N	type
2. C₂×#11718156	C₂	semidirect
4. #13112927	C₂	semidirect
11. C₁₃×#467	C₄	semidirect
135. #467	Dic₁₃	semidirect
236. C₁₃	#12994	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718767	2
C₂×#11718156	2
C₂×C₂²⋊#6090	2
#13112927	2
C₂×C₁₃×#467	2
#12994	13