Subgroups — #15777964

Order 3328.

490 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718350	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718106	C₂	1	2	yes	maximal
3	C₄×#88052	C₂	1	1	yes	maximal, characteristic, complemented
4	#13112919	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#6094	C₂²	1	1	yes	characteristic
7	C₂²×C₈×D₁₃	C₄	1	1	yes	characteristic
8	C₂×#88126	C₄	1	1	yes	characteristic
9	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×#88055	C₂²	1	1	yes	characteristic
12	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
13	C₂×#88052	C₂²	1	2	yes	—
14	C₂×#88043	C₄	1	1	yes	characteristic
15	#11718350	—	2	1	no	—
16	#11718350	—	2	1	no	—
17	#11718350	—	2	1	no	—
18	#11718350	—	2	1	no	—
19	C₁₃×#346	—	2	1	no	—
20	C₄×C₁₃×C₁₆	—	2	1	no	—
21	#11718106	C₄	1	8	yes	complemented
22	#11718053	—	2	1	no	—
23	C₄×#6090	—	2	1	no	—
24	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
27	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂×#6103	C₈	1	2	yes	—
29	C₂×#6101	C₈	1	2	yes	—
30	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
32	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
33	C₂×#6094	—	2	1	no	—
34	C₂×#6094	—	2	1	no	—
35	C₂×#6094	—	2	2	no	—
36	C₂×#6094	C₂×C₄	1	4	yes	—
37	C₂×C₈×D₁₃	—	2	1	no	—
38	C₂×C₈×D₁₃	—	2	1	no	—
39	C₂×C₈×D₁₃	—	2	2	no	—
40	C₂×C₈×D₁₃	C₈	1	4	yes	—
41	#88126	—	2	1	no	—
42	#88126	—	2	1	no	—
43	#88126	—	2	2	no	—
44	C₁₃×M₃₂	—	2	2	no	—
45	C₁₃×M₃₂	C₂×C₄	1	4	yes	—
46	C₂×C₁₃×C₁₆	—	2	2	no	—
47	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
48	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
49	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
50	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
51	#88055	—	2	1	no	—
52	#88055	—	2	1	no	—
53	C₈×Dic₁₃	—	2	1	no	—
54	C₈×Dic₁₃	—	2	1	no	—
55	#88052	—	2	2	no	—
56	#88052	C₂×C₄	1	4	yes	—
57	C₂×#6090	—	2	2	no	—
58	#88043	—	2	1	no	—
59	#88043	—	2	1	no	—
60	#12602	—	13	1	no	maximal, Sylow
61	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
62	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
63	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
64	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
65	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
66	C₂×C₄×D₁₃	—	2	1	no	—
67	C₂×C₄×D₁₃	—	2	1	no	—
68	C₂×C₄×D₁₃	—	2	1	no	—
69	C₂×C₄×D₁₃	—	2	1	no	—
70	C₂×C₄×D₁₃	C₄²	1	2	yes	—
71	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
72	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
75	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
76	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
77	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
78	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
79	C₂×C₈×C₁₃	#41	1	2	yes	—
80	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₄²×C₁₃	M₁₆	1	2	yes	—
83	#6103	—	2	2	no	—
84	#6103	—	2	2	no	—
85	#6101	—	2	2	no	—
86	#6101	—	2	2	no	—
87	C₄×Dic₁₃	—	2	1	no	—
88	C₄×Dic₁₃	—	2	1	no	—
89	C₂×#1055	—	2	1	no	—
90	C₂×#1055	—	2	1	no	—
91	C₂×#1055	—	2	1	no	—
92	C₂×#1055	—	2	1	no	—
93	C₂×#1055	C₄²	1	2	yes	—
94	C₂×#1055	C₂×C₈	1	2	yes	—
95	#6094	—	2	4	no	—
96	#6094	—	2	4	no	—
97	C₈×D₁₃	—	2	4	no	—
98	C₈×D₁₃	—	2	4	no	—
99	C₁₃×C₁₆	—	2	4	no	—
100	#6090	—	2	4	no	—
101	C₂×#405	—	13	1	no	—
102	C₂×#349	—	13	2	no	—
103	C₄×M₃₂	—	13	1	no	—
104	C₄×M₃₂	D₁₃	1	1	yes	characteristic, complemented
105	#1377	—	13	2	no	—
106	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
107	C₂²×D₁₃	—	2	1	no	—
108	C₂²×D₁₃	—	2	1	no	—
109	C₂²×D₁₃	—	4	2	no	—
110	C₂²×D₁₃	C₄×C₈	1	2	yes	—
111	C₂×C₄×C₁₃	—	4	2	no	—
112	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
113	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
114	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
115	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
116	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
117	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
118	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
119	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
120	C₂×Dic₁₃	—	2	1	no	—
121	C₂×Dic₁₃	—	2	1	no	—
122	C₂×Dic₁₃	—	2	2	no	—
123	C₂×Dic₁₃	—	4	2	no	—
124	C₂×Dic₁₃	C₄×C₈	1	2	yes	—
125	C₄×D₁₃	—	2	2	no	—
126	C₄×D₁₃	—	2	2	no	—
127	C₄×D₁₃	—	2	2	no	—
128	C₄×D₁₃	—	2	2	no	—
129	C₈×C₁₃	C₂²⋊C₈	1	2	yes	—
130	C₈×C₁₃	C₂²⋊C₈	1	2	yes	—
131	C₈×C₁₃	C₄×D₄	1	2	yes	—
132	C₈×C₁₃	C₄×D₄	1	2	yes	—
133	#1055	—	2	2	no	—
134	#1055	—	2	2	no	—
135	C₂²×M₁₆	—	13	1	no	—
136	C₂³×C₈	—	13	1	no	—
137	C₂×#117	—	13	1	no	—
138	C₂×M₃₂	—	13	2	no	—
139	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
140	#405	—	26	1	no	—
141	#405	—	26	1	no	—
142	#405	—	26	1	no	—
143	#405	—	26	1	no	—
144	C₂×#97	—	13	1	no	—
145	C₂×#97	—	13	1	no	—
146	C₂×C₄×C₈	—	13	1	no	—
147	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
148	#349	—	13	8	no	—
149	#346	—	2	1	no	—
150	#346	—	26	1	no	—
151	C₄×C₁₆	—	2	1	no	—
152	C₄×C₁₆	—	26	1	no	—
153	C₂²×C₁₃	—	2	2	no	—
154	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
155	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
156	C₂²×C₁₃	#431	1	1	yes	characteristic
157	C₂×D₁₃	—	2	2	no	—
158	C₂×D₁₃	—	4	2	no	—
159	C₂×D₁₃	—	4	2	no	—
160	C₂×D₁₃	—	4	2	no	—
161	C₄×C₁₃	—	2	2	no	—
162	C₄×C₁₃	—	2	2	no	—
163	C₄×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
164	C₄×C₁₃	C₄×M₁₆	1	1	yes	characteristic
165	C₄×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
166	C₄×C₁₃	#431	1	1	yes	characteristic
167	Dic₁₃	—	2	2	no	—
168	Dic₁₃	—	4	2	no	—
169	C₂³×C₄	—	13	1	no	—
170	C₂×M₁₆	—	13	4	no	—
171	C₂×M₁₆	—	26	1	no	—
172	C₂×M₁₆	—	26	2	no	—
173	C₂×M₁₆	—	26	1	no	—
174	C₂²×C₈	—	13	1	no	—
175	C₂²×C₈	—	13	1	no	—
176	C₂²×C₈	—	13	4	no	—
177	C₂²×C₈	—	26	2	no	—
178	C₂²×C₈	—	26	1	no	—
179	C₂²×C₈	—	26	1	no	—
180	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
181	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
182	#117	—	26	2	no	—
183	#117	—	26	1	no	—
184	#117	—	26	1	no	—
185	C₂×C₄⋊C₄	—	13	2	no	—
186	C₂×C₂²⋊C₄	—	13	2	no	—
187	C₂×C₄²	—	13	1	no	—
188	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
189	M₃₂	—	2	2	no	—
190	M₃₂	—	13	4	no	—
191	M₃₂	—	26	2	no	—
192	M₃₂	C₄×D₁₃	1	4	yes	—
193	C₂×C₁₆	—	2	2	no	—
194	C₂×C₁₆	—	26	2	no	—
195	#97	—	26	1	no	—
196	#97	—	26	1	no	—
197	#97	—	26	1	no	—
198	#97	—	26	1	no	—
199	C₄×C₈	—	26	1	no	—
200	C₄×C₈	—	26	1	no	—
201	C₄×C₈	D₅₂	1	1	yes	characteristic
202	C₄×C₈	D₅₂	1	1	yes	characteristic
203	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
204	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
205	C₂×C₁₃	—	2	1	no	—
206	C₂×C₁₃	—	2	1	no	—
207	C₂×C₁₃	C₄×C₂²⋊C₈	1	1	yes	characteristic
208	C₂×C₁₃	#2115	1	2	yes	—
209	D₁₃	—	4	2	no	—
210	C₂⁴	—	13	1	no	—
211	C₂²×C₄	—	13	1	no	—
212	C₂²×C₄	—	13	2	no	—
213	C₂²×C₄	—	13	2	no	—
214	C₂²×C₄	—	13	2	no	—
215	C₂²×C₄	—	26	1	no	—
216	C₂²×C₄	—	26	1	no	—
217	C₂²×C₄	—	26	1	no	—
218	C₂²×C₄	—	26	1	no	—
219	C₂²×C₄	C₈×D₁₃	1	2	yes	—
220	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
221	M₁₆	—	26	4	no	—
222	M₁₆	—	26	4	no	—
223	C₂×C₈	—	13	2	no	—
224	C₂×C₈	—	13	2	no	—
225	C₂×C₈	—	26	1	no	—
226	C₂×C₈	—	26	1	no	—
227	C₂×C₈	—	26	1	no	—
228	C₂×C₈	—	26	1	no	—
229	C₂×C₈	—	26	4	no	—
230	C₂×C₈	—	26	4	no	—
231	C₂×C₈	C₈×D₁₃	1	2	yes	—
232	C₂×C₈	#6094	1	2	yes	—
233	C₂×C₈	#6103	1	1	yes	characteristic
234	C₂×C₈	#6103	1	1	yes	characteristic
235	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
236	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
237	C₂×C₈	#6127	1	2	yes	—
238	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
239	C₄⋊C₄	—	26	2	no	—
240	C₄⋊C₄	—	26	2	no	—
241	C₂²⋊C₄	—	26	2	no	—
242	C₂²⋊C₄	—	26	2	no	—
243	C₄²	—	26	1	no	—
244	C₄²	—	26	1	no	—
245	C₄²	#6094	1	2	yes	—
246	C₄²	#6103	1	1	yes	characteristic
247	C₄²	#6103	1	1	yes	characteristic
248	C₁₆	—	2	4	no	—
249	C₁₆	—	26	4	no	—
250	C₁₃	#12602	1	1	yes	characteristic, complemented, Sylow
251	C₂³	—	13	2	no	—
252	C₂³	—	26	1	no	—
253	C₂³	—	26	1	no	—
254	C₂³	—	52	2	no	—
255	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
256	C₂×C₄	—	4	2	no	—
257	C₂×C₄	—	13	2	no	—
258	C₂×C₄	—	26	1	no	—
259	C₂×C₄	—	26	1	no	—
260	C₂×C₄	—	26	2	no	—
261	C₂×C₄	—	26	2	no	—
262	C₂×C₄	—	26	2	no	—
263	C₂×C₄	—	26	2	no	—
264	C₂×C₄	—	26	2	no	—
265	C₂×C₄	—	52	2	no	—
266	C₂×C₄	#88060	1	2	yes	—
267	C₂×C₄	#88060	1	2	yes	—
268	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
269	C₂×C₄	#88126	1	1	yes	characteristic
270	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
271	C₂×C₄	C₂×#6094	1	1	yes	characteristic
272	C₂×C₄	C₂×#6094	1	1	yes	characteristic
273	C₂×C₄	C₂×#6103	1	1	yes	characteristic
274	C₈	—	26	2	no	—
275	C₈	—	26	2	no	—
276	C₈	#88060	1	2	yes	—
277	C₈	#88060	1	2	yes	—
278	C₈	C₄×D₅₂	1	2	yes	—
279	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
280	C₂²	—	2	2	no	—
281	C₂²	—	26	2	no	—
282	C₂²	—	52	2	no	—
283	C₂²	—	52	2	no	—
284	C₂²	—	52	2	no	—
285	C₂²	C₄×C₈×D₁₃	1	1	yes	characteristic
286	C₂²	#11718346	1	1	yes	characteristic
287	C₂²	C₂×#88060	1	1	yes	characteristic
288	C₄	—	2	2	no	—
289	C₄	—	2	2	no	—
290	C₄	—	26	2	no	—
291	C₄	—	52	2	no	—
292	C₄	#11718346	1	1	yes	characteristic
293	C₄	C₄×#6094	1	1	yes	characteristic
294	C₄	C₄×#6103	1	1	yes	characteristic
295	C₄	C₂×#88060	1	1	yes	characteristic
296	C₂	—	2	1	no	—
297	C₂	—	2	1	no	—
298	C₂	—	52	2	no	—
299	C₂	C₄×#88060	1	1	yes	characteristic
300	C₂	#13116456	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	#6103
commutator	C₂²×C₁₃	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₄×C₁₃×M₃₂	C₂
socle	C₂²×C₁₃	C₂×C₂²⋊C₈
prime radical	C₂³×D₁₃	C₂×C₈
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₄×M₃₂	D₁₃
hypocenter	C₁₃	#12602
LCS	G ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
3. C₄×#88052	C₂	semidirect
4. #13112919	C₂	semidirect
5. C₄×C₁₃×M₃₂	C₂	semidirect
21. #11718106	C₄	semidirect
104. C₄×M₃₂	D₁₃	semidirect
250. C₁₃	#12602	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718350	2
C₂×#11718106	2
C₄×#88052	2
#13112919	2
C₄×C₁₃×M₃₂	2
#12602	13