Subgroups — #15860892

Order 3328.

1110 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718585	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718762	C₂	1	2	yes	maximal
3	#13117243	C₂	1	1	yes	maximal, characteristic
4	#13114708	C₂	1	8	yes	maximal, complemented
5	#13114532	C₂	1	2	yes	maximal
6	C₂²×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×#88180	C₂²	1	2	yes	—
11	C₂²×#6099	C₂²	1	2	yes	—
12	C₂×C₁₃×#97	C₄	1	8	yes	complemented
13	C₂×C₁₃×#97	C₂²	1	4	yes	—
14	#11718873	C₄	1	4	yes	—
15	#11718762	—	2	8	no	—
16	C₂×#88055	C₂²	1	4	yes	—
17	C₂×C₈×Dic₁₃	C₂²	1	4	yes	—
18	#11718597	C₄	1	2	yes	—
19	#11718596	C₄	1	2	yes	—
20	C₄×C₄⋊Dic₁₃	C₂²	1	4	yes	—
21	#11718585	C₄	1	8	yes	complemented
22	C₂×C₄⋊#1055	C₂²	1	4	yes	—
23	#11718142	C₂²	1	8	yes	—
24	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
25	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
26	C₂²×C₈×C₁₃	—	2	2	no	—
27	C₂²×C₈×C₁₃	—	2	2	no	—
28	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
29	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
30	C₂²×C₈×C₁₃	D₄	1	4	yes	—
31	C₂²×C₈×C₁₃	Q₈	1	4	yes	—
32	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
33	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
34	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
37	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
38	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
39	C₂×C₂²⋊Dic₁₃	C₂×C₄	1	4	yes	—
40	#88180	—	2	4	no	—
41	#88180	—	2	4	no	—
42	C₂×C₄⋊Dic₁₃	C₂×C₄	1	4	yes	—
43	C₂×C₄⋊Dic₁₃	C₂×C₄	1	8	yes	—
44	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
45	C₂×#6099	—	2	4	no	—
46	C₂×#6099	—	2	4	no	—
47	C₂×#6099	C₂×C₄	1	8	yes	—
48	C₂²×#1055	C₂³	1	4	yes	—
49	C₁₃×#97	C₂×C₄	1	16	yes	—
50	#88071	C₂×C₄	1	8	yes	—
51	#88055	—	2	8	no	—
52	C₈×Dic₁₃	—	2	8	no	—
53	C₄⋊#1055	C₂×C₄	1	16	yes	—
54	#20438	—	13	1	no	maximal, Sylow
55	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	—	4	4	no	—
57	C₂²×C₄×C₁₃	C₄²	1	8	yes	—
58	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
59	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
60	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
62	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
63	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
64	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
65	C₂²×C₄×C₁₃	#41	1	2	yes	—
66	C₂²×C₄×C₁₃	#41	1	2	yes	—
67	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
68	C₂²×Dic₁₃	C₂²×C₄	1	8	yes	—
69	C₂×C₈×C₁₃	—	2	8	no	—
70	C₂×C₈×C₁₃	—	2	2	no	—
71	C₂×C₈×C₁₃	—	2	2	no	—
72	C₂×C₈×C₁₃	C₄⋊C₄	1	16	yes	complemented
73	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
74	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
75	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
76	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
77	C₄²×C₁₃	C₄²	1	4	yes	—
78	C₄²×C₁₃	C₄²	1	4	yes	—
79	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
80	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
81	C₂²⋊Dic₁₃	—	2	8	no	—
82	C₄⋊Dic₁₃	—	2	8	no	—
83	C₄⋊Dic₁₃	—	4	8	no	—
84	C₄×Dic₁₃	—	2	4	no	—
85	C₄×Dic₁₃	—	2	4	no	—
86	#6099	—	2	16	no	—
87	C₂×#1055	—	2	4	no	—
88	C₂×#1055	—	2	4	no	—
89	C₂×#1055	C₂²×C₄	1	8	yes	—
90	C₂×#423	—	13	1	no	—
91	C₂×#405	—	13	2	no	—
92	C₂²×#97	D₁₃	1	1	yes	characteristic
93	#2285	—	13	1	no	—
94	#1771	—	13	8	no	—
95	#1729	—	13	2	no	—
96	C₂³×C₁₃	—	2	4	no	—
97	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
98	C₂³×C₁₃	C₄×D₄	1	2	yes	—
99	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
100	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
101	C₂×C₄×C₁₃	—	2	4	no	—
102	C₂×C₄×C₁₃	—	2	4	no	—
103	C₂×C₄×C₁₃	—	4	8	no	—
104	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
105	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
106	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
107	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
108	C₂×C₄×C₁₃	#117	1	4	yes	—
109	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
110	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
111	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
112	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
113	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
114	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
115	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
116	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
117	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
118	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
119	C₂×Dic₁₃	—	2	8	no	—
120	C₂×Dic₁₃	—	2	16	no	—
121	C₈×C₁₃	—	2	4	no	—
122	C₈×C₁₃	C₂×C₄⋊C₄	1	8	yes	—
123	#1055	—	2	8	no	—
124	C₂²×M₁₆	—	13	2	no	—
125	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
126	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
127	C₂×#117	—	13	2	no	—
128	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
129	#423	—	13	8	no	—
130	C₂×C₄⋊C₈	—	13	4	no	—
131	#405	—	26	8	no	—
132	C₂×#97	—	13	4	no	—
133	C₂×#97	Dic₁₃	1	8	yes	complemented
134	C₂×#97	C₂×D₁₃	1	4	yes	—
135	C₂×C₄×C₈	—	13	4	no	—
136	#384	—	13	2	no	—
137	#382	—	13	2	no	—
138	#380	—	13	4	no	—
139	C₄×C₄⋊C₄	—	13	4	no	—
140	#336	—	13	8	no	—
141	C₂²×C₁₃	—	2	4	no	—
142	C₂²×C₁₃	—	2	4	no	—
143	C₂²×C₁₃	—	2	4	no	—
144	C₂²×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
145	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
146	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
147	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
148	C₂²×C₁₃	#568	1	4	yes	—
149	C₄×C₁₃	—	2	4	no	—
150	C₄×C₁₃	—	2	4	no	—
151	C₄×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
152	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
153	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
154	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
155	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
156	Dic₁₃	—	4	8	no	—
157	C₂³×C₄	C₄×D₁₃	1	2	yes	—
158	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
159	C₂×M₁₆	—	13	8	no	—
160	C₂×M₁₆	—	26	4	no	—
161	C₂×M₁₆	—	26	4	no	—
162	C₂²×C₈	—	2	2	no	—
163	C₂²×C₈	—	2	2	no	—
164	C₂²×C₈	—	13	4	no	—
165	C₂²×C₈	Dic₂₆	1	4	yes	—
166	C₂²×C₈	D₅₂	1	4	yes	—
167	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
168	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
169	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
170	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
171	#117	—	26	4	no	—
172	#117	—	26	4	no	—
173	C₂×C₄⋊C₄	—	13	4	no	—
174	C₂×C₄⋊C₄	—	13	8	no	—
175	C₂×C₂²⋊C₄	—	13	4	no	—
176	C₂×C₄²	—	13	4	no	—
177	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
178	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
179	C₂×C₄²	C₄×D₁₃	1	4	yes	—
180	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
181	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
182	C₄⋊C₈	—	13	16	no	—
183	#97	—	26	8	no	—
184	#97	C₂×Dic₁₃	1	16	yes	—
185	C₄×C₈	—	26	8	no	—
186	#95	—	13	8	no	—
187	C₂×C₁₃	—	2	4	no	—
188	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₁₃	#2873	1	2	yes	—
190	C₂×C₁₃	#2932	1	2	yes	—
191	C₂×C₁₃	#2961	1	2	yes	—
192	C₂⁴	C₂×C₄×D₁₃	1	1	yes	characteristic
193	C₂²×C₄	—	4	4	no	—
194	C₂²×C₄	—	13	8	no	—
195	C₂²×C₄	C₄×Dic₁₃	1	8	yes	—
196	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
197	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
198	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
199	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
200	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
201	C₂²×C₄	C₂×D₅₂	1	2	yes	—
202	C₂²×C₄	#6127	1	2	yes	—
203	C₂²×C₄	#6127	1	2	yes	—
204	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
205	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
206	M₁₆	—	26	16	no	—
207	C₂×C₈	—	2	8	no	—
208	C₂×C₈	—	2	2	no	—
209	C₂×C₈	—	2	2	no	—
210	C₂×C₈	—	13	8	no	—
211	C₂×C₈	—	26	4	no	—
212	C₂×C₈	—	26	4	no	—
213	C₂×C₈	C₄⋊Dic₁₃	1	16	yes	complemented
214	C₂×C₈	C₂×Dic₂₆	1	4	yes	—
215	C₂×C₈	C₂×D₅₂	1	4	yes	—
216	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
217	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
218	C₄⋊C₄	—	26	8	no	—
219	C₄⋊C₄	—	52	8	no	—
220	C₂²⋊C₄	—	26	8	no	—
221	C₄²	—	26	4	no	—
222	C₄²	—	26	4	no	—
223	C₄²	C₄×Dic₁₃	1	4	yes	—
224	C₄²	C₄×Dic₁₃	1	4	yes	—
225	C₄²	C₂×C₄×D₁₃	1	4	yes	—
226	C₄²	C₂²×Dic₁₃	1	4	yes	—
227	C₁₃	#20438	1	1	yes	characteristic, complemented, Sylow
228	C₂³	—	2	4	no	—
229	C₂³	C₄×Dic₂₆	1	2	yes	—
230	C₂³	C₄×D₅₂	1	2	yes	—
231	C₂³	C₂×C₄×Dic₁₃	1	2	yes	—
232	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
233	C₂×C₄	—	2	4	no	—
234	C₂×C₄	—	2	4	no	—
235	C₂×C₄	—	4	8	no	—
236	C₂×C₄	—	26	8	no	—
237	C₂×C₄	—	26	16	no	—
238	C₂×C₄	C₄×Dic₂₆	1	4	yes	—
239	C₂×C₄	C₄×Dic₂₆	1	2	yes	—
240	C₂×C₄	C₄×D₅₂	1	4	yes	—
241	C₂×C₄	C₄×D₅₂	1	2	yes	—
242	C₂×C₄	C₂×C₄×Dic₁₃	1	4	yes	—
243	C₂×C₄	C₂×C₄×Dic₁₃	1	4	yes	—
244	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
245	C₂×C₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
246	C₂×C₄	#88180	1	4	yes	—
247	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
248	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
249	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
250	C₂×C₄	C₂×#6127	1	1	yes	characteristic
251	C₂×C₄	C₂×#6127	1	1	yes	characteristic
252	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
253	C₈	—	2	4	no	—
254	C₈	—	26	8	no	—
255	C₈	C₂×C₄⋊Dic₁₃	1	8	yes	—
256	C₂²	—	2	4	no	—
257	C₂²	—	2	4	no	—
258	C₂²	—	2	4	no	—
259	C₂²	C₄×C₄⋊Dic₁₃	1	4	yes	—
260	C₂²	C₂×C₄×Dic₂₆	1	1	yes	characteristic
261	C₂²	C₂×C₄×D₅₂	1	1	yes	characteristic
262	C₂²	#11719450	1	4	yes	—
263	C₂²	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
264	C₄	—	2	4	no	—
265	C₄	—	2	4	no	—
266	C₄	—	52	8	no	—
267	C₄	C₄×C₄⋊Dic₁₃	1	4	yes	—
268	C₄	C₂×C₄×Dic₂₆	1	1	yes	characteristic
269	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
270	C₄	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
271	C₄	C₂×#88180	1	1	yes	characteristic
272	C₂	—	2	4	no	—
273	C₂	C₂×C₄×C₄⋊Dic₁₃	1	1	yes	characteristic
274	C₂	#13123254	1	2	yes	—
275	C₂	#13123555	1	2	yes	—
276	C₂	#13123776	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator	C₂²×C₁₃	C₂²×C₄²
Fitting	C₂²×C₁₃×#97	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂²×#97	D₁₃
hypocenter	C₁₃	#20438
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
4. #13114708	C₂	semidirect
12. C₂×C₁₃×#97	C₄	semidirect
21. #11718585	C₄	semidirect
72. C₂×C₈×C₁₃	C₄⋊C₄	semidirect
133. C₂×#97	Dic₁₃	semidirect
213. C₂×C₈	C₄⋊Dic₁₃	semidirect
227. C₁₃	#20438	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718585	2
C₂×#11718762	2
#13117243	2
#13114708	2
#13114532	2
C₂²×C₁₃×#97	2
#20438	13