Subgroups — C₁₃₁×#22899 #45708783

Order 33536.

1016 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3018×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2956×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2901×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#1962×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#1932×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1906×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#1884×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1861×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	C₄×#104×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#585×C₁₃₁	C₂²	1	1	yes	characteristic
11	#575×C₁₃₁	C₂²	1	2	yes	—
12	#568×C₁₃₁	C₂²	1	2	yes	—
13	#568×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
14	#532×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₄×#41×C₁₃₁	C₂²	1	2	yes	—
16	#456×C₁₃₁	C₄	1	2	yes	complemented
17	#455×C₁₃₁	C₄	1	2	yes	complemented
18	#454×C₁₃₁	C₄	1	2	yes	complemented
19	#453×C₁₃₁	C₄	1	2	yes	complemented
20	#444×C₁₃₁	—	2	4	no	—
21	#443×C₁₃₁	—	2	4	no	—
22	#430×C₁₃₁	C₂²	1	2	yes	complemented
23	#423×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
24	#421×C₁₃₁	—	2	4	no	—
25	#421×C₁₃₁	C₂²	1	2	yes	—
26	#421×C₁₃₁	C₂²	1	2	yes	—
27	C₂×#104×C₁₃₁	—	2	4	no	—
28	C₂×#104×C₁₃₁	C₂²	1	2	yes	—
29	C₂×#104×C₁₃₁	C₂²	1	2	yes	—
30	C₂×#104×C₁₃₁	C₂²	1	2	yes	—
31	C₂×#104×C₁₃₁	C₂²	1	2	yes	complemented
32	#413×C₁₃₁	C₂²	1	1	yes	characteristic
33	#410×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
34	C₄×M₁₆×C₁₃₁	C₂²	1	2	yes	complemented
35	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
36	#344×C₁₃₁	C₂²	1	2	yes	complemented
37	#339×C₁₃₁	C₂²	1	2	yes	complemented
38	#339×C₁₃₁	C₂²	1	2	yes	complemented
39	2₋¹⁺⁴×C₁₃₁	—	2	2	no	—
40	2₋¹⁺⁴×C₁₃₁	C₂×C₄	1	2	yes	—
41	H(5,𝔽₂)×C₁₃₁	—	2	2	no	—
42	H(5,𝔽₂)×C₁₃₁	—	4	1	no	—
43	H(5,𝔽₂)×C₁₃₁	C₂×C₄	1	2	yes	—
44	C₂×#41×C₁₃₁	—	2	4	no	—
45	C₂×#41×C₁₃₁	—	4	1	no	—
46	C₂×#41×C₁₃₁	C₂³	1	1	yes	characteristic
47	C₂×#41×C₁₃₁	C₂³	1	1	yes	characteristic
48	C₂×#41×C₁₃₁	C₂³	1	2	yes	—
49	#137×C₁₃₁	—	2	2	no	—
50	#137×C₁₃₁	C₂×C₄	1	4	yes	complemented
51	AGL(1,ℤ/8)×C₁₃₁	—	2	2	no	—
52	AGL(1,ℤ/8)×C₁₃₁	C₂×C₄	1	4	yes	complemented
53	#135×C₁₃₁	—	2	4	no	—
54	#131×C₁₃₁	—	2	4	no	—
55	#131×C₁₃₁	—	2	4	no	—
56	#131×C₁₃₁	—	4	2	no	—
57	C₂×M₁₆×C₁₃₁	—	2	4	no	—
58	C₂×M₁₆×C₁₃₁	—	4	1	no	—
59	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
60	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
61	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
62	C₄⋊Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic, complemented
63	#127×C₁₃₁	C₂×C₄	1	1	yes	characteristic, complemented
64	#124×C₁₃₁	C₂×C₄	1	1	yes	characteristic, complemented
65	#124×C₁₃₁	C₂×C₄	1	1	yes	characteristic, complemented
66	#121×C₁₃₁	—	4	1	no	—
67	C₄×Q₈×C₁₃₁	—	2	2	no	—
68	C₄×D₄×C₁₃₁	—	2	2	no	—
69	C₄×D₄×C₁₃₁	—	4	1	no	—
70	C₄×D₄×C₁₃₁	—	4	2	no	—
71	#117×C₁₃₁	—	2	2	no	—
72	#117×C₁₃₁	C₂³	1	2	yes	—
73	C₂×C₄²×C₁₃₁	—	2	2	no	—
74	C₂×C₄²×C₁₃₁	—	4	1	no	—
75	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
77	#108×C₁₃₁	—	2	4	no	—
78	C₄⋊C₈×C₁₃₁	—	4	1	no	—
79	#104×C₁₃₁	—	2	4	no	—
80	#104×C₁₃₁	—	2	4	no	—
81	#104×C₁₃₁	—	2	2	no	—
82	#104×C₁₃₁	—	2	2	no	—
83	#104×C₁₃₁	—	2	2	no	—
84	#104×C₁₃₁	—	2	2	no	—
85	#104×C₁₃₁	C₂×C₄	1	4	yes	complemented
86	#104×C₁₃₁	C₂×C₄	1	4	yes	complemented
87	#104×C₁₃₁	D₄	1	4	yes	complemented
88	#104×C₁₃₁	D₄	1	4	yes	complemented
89	#101×C₁₃₁	C₂×C₄	1	2	yes	complemented
90	#100×C₁₃₁	C₂×C₄	1	2	yes	complemented
91	#99×C₁₃₁	—	4	1	no	—
92	#97×C₁₃₁	—	2	2	no	—
93	C₄×C₈×C₁₃₁	—	2	2	no	—
94	#41×C₁₃₁	—	2	2	no	—
95	#41×C₁₃₁	—	2	2	no	—
96	#41×C₁₃₁	—	2	4	no	—
97	#41×C₁₃₁	—	2	4	no	—
98	#41×C₁₃₁	—	2	2	no	—
99	#41×C₁₃₁	—	2	2	no	—
100	#41×C₁₃₁	—	2	2	no	—
101	#41×C₁₃₁	—	2	2	no	—
102	#41×C₁₃₁	—	4	2	no	—
103	#41×C₁₃₁	—	4	2	no	—
104	#41×C₁₃₁	—	4	4	no	—
105	#41×C₁₃₁	—	4	2	no	—
106	#41×C₁₃₁	C₂²×C₄	1	4	yes	—
107	#41×C₁₃₁	C₂×D₄	1	4	yes	—
108	C₂×Q₈×C₁₃₁	—	2	4	no	—
109	C₂×Q₈×C₁₃₁	—	4	1	no	—
110	C₂×Q₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
111	C₂×Q₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
112	C₂×Q₈×C₁₃₁	#41	1	2	yes	—
113	C₂×D₄×C₁₃₁	—	2	2	no	—
114	C₂×D₄×C₁₃₁	—	2	4	no	—
115	C₂×D₄×C₁₃₁	—	2	1	no	—
116	C₂×D₄×C₁₃₁	—	2	1	no	—
117	C₂×D₄×C₁₃₁	—	4	1	no	—
118	C₂×D₄×C₁₃₁	—	4	2	no	—
119	C₂×D₄×C₁₃₁	—	4	1	no	—
120	C₂×D₄×C₁₃₁	—	4	4	no	—
121	C₂×D₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
122	C₂×D₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
123	C₂×D₄×C₁₃₁	#41	1	2	yes	—
124	C₂²×C₄×C₁₃₁	—	2	2	no	—
125	C₂²×C₄×C₁₃₁	—	2	2	no	—
126	C₂²×C₄×C₁₃₁	—	2	1	no	—
127	C₂²×C₄×C₁₃₁	—	2	1	no	—
128	C₂²×C₄×C₁₃₁	—	2	1	no	—
129	C₂²×C₄×C₁₃₁	—	4	2	no	—
130	C₂²×C₄×C₁₃₁	—	4	2	no	—
131	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
132	Q₁₆×C₁₃₁	—	2	4	no	—
133	SD₁₆×C₁₃₁	—	2	4	no	—
134	SD₁₆×C₁₃₁	—	2	4	no	—
135	D₈×C₁₃₁	—	2	4	no	—
136	M₁₆×C₁₃₁	—	2	2	no	—
137	M₁₆×C₁₃₁	—	2	2	no	—
138	M₁₆×C₁₃₁	—	2	2	no	—
139	M₁₆×C₁₃₁	—	2	2	no	—
140	M₁₆×C₁₃₁	—	4	2	no	—
141	M₁₆×C₁₃₁	—	4	4	no	—
142	M₁₆×C₁₃₁	C₂²×C₄	1	4	yes	—
143	M₁₆×C₁₃₁	C₂×D₄	1	4	yes	—
144	C₂×C₈×C₁₃₁	—	2	2	no	—
145	C₂×C₈×C₁₃₁	—	2	2	no	—
146	C₂×C₈×C₁₃₁	—	2	2	no	—
147	C₂×C₈×C₁₃₁	—	4	2	no	—
148	C₂×C₈×C₁₃₁	—	4	4	no	—
149	C₄⋊C₄×C₁₃₁	—	2	2	no	—
150	C₄⋊C₄×C₁₃₁	—	4	1	no	—
151	C₄⋊C₄×C₁₃₁	—	4	2	no	—
152	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
153	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
154	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
155	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
156	C₄²×C₁₃₁	—	2	2	no	—
157	C₄²×C₁₃₁	—	2	1	no	—
158	C₄²×C₁₃₁	—	2	2	no	—
159	C₄²×C₁₃₁	—	4	2	no	—
160	C₄²×C₁₃₁	—	4	4	no	—
161	C₄²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
164	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
165	C₂³×C₁₃₁	—	2	2	no	—
166	C₂³×C₁₃₁	—	2	1	no	—
167	C₂³×C₁₃₁	—	2	1	no	—
168	C₂³×C₁₃₁	—	4	2	no	—
169	C₂³×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
170	Q₈×C₁₃₁	—	2	2	no	—
171	Q₈×C₁₃₁	—	2	2	no	—
172	Q₈×C₁₃₁	—	2	2	no	—
173	Q₈×C₁₃₁	—	4	2	no	—
174	Q₈×C₁₃₁	C₄×D₄	1	4	yes	—
175	D₄×C₁₃₁	—	2	4	no	—
176	D₄×C₁₃₁	—	2	4	no	—
177	D₄×C₁₃₁	—	2	2	no	—
178	D₄×C₁₃₁	—	2	2	no	—
179	D₄×C₁₃₁	—	2	2	no	—
180	D₄×C₁₃₁	—	4	4	no	—
181	D₄×C₁₃₁	—	4	2	no	—
182	D₄×C₁₃₁	—	4	2	no	—
183	D₄×C₁₃₁	—	4	2	no	—
184	D₄×C₁₃₁	—	8	2	no	—
185	D₄×C₁₃₁	C₄×D₄	1	4	yes	—
186	C₂×C₄×C₁₃₁	—	2	1	no	—
187	C₂×C₄×C₁₃₁	—	2	2	no	—
188	C₂×C₄×C₁₃₁	—	2	2	no	—
189	C₂×C₄×C₁₃₁	—	2	4	no	—
190	C₂×C₄×C₁₃₁	—	2	4	no	—
191	C₂×C₄×C₁₃₁	—	2	1	no	—
192	C₂×C₄×C₁₃₁	—	2	1	no	—
193	C₂×C₄×C₁₃₁	—	2	1	no	—
194	C₂×C₄×C₁₃₁	—	2	2	no	—
195	C₂×C₄×C₁₃₁	—	4	2	no	—
196	C₂×C₄×C₁₃₁	—	4	4	no	—
197	C₂×C₄×C₁₃₁	—	4	4	no	—
198	C₂×C₄×C₁₃₁	—	4	2	no	—
199	C₂×C₄×C₁₃₁	—	4	1	no	—
200	C₂×C₄×C₁₃₁	—	4	1	no	—
201	C₂×C₄×C₁₃₁	—	4	1	no	—
202	C₂×C₄×C₁₃₁	—	4	1	no	—
203	C₂×C₄×C₁₃₁	—	4	2	no	—
204	C₂×C₄×C₁₃₁	—	8	4	no	—
205	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
207	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
208	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
209	C₈×C₁₃₁	—	2	4	no	—
210	C₈×C₁₃₁	—	2	4	no	—
211	C₈×C₁₃₁	—	4	2	no	—
212	C₂²×C₁₃₁	—	2	4	no	—
213	C₂²×C₁₃₁	—	4	1	no	—
214	C₂²×C₁₃₁	—	4	1	no	—
215	C₂²×C₁₃₁	—	4	1	no	—
216	C₂²×C₁₃₁	—	8	2	no	—
217	C₂²×C₁₃₁	—	8	1	no	—
218	C₂²×C₁₃₁	—	8	1	no	—
219	C₂²×C₁₃₁	—	16	2	no	—
220	C₂²×C₁₃₁	#518	1	1	yes	characteristic
221	C₂²×C₁₃₁	#546	1	2	yes	—
222	C₄×C₁₃₁	—	2	4	no	—
223	C₄×C₁₃₁	—	2	2	no	—
224	C₄×C₁₃₁	—	2	4	no	—
225	C₄×C₁₃₁	—	4	2	no	—
226	C₄×C₁₃₁	—	4	1	no	—
227	C₄×C₁₃₁	—	4	1	no	—
228	C₄×C₁₃₁	—	4	1	no	—
229	C₄×C₁₃₁	—	8	2	no	—
230	C₄×C₁₃₁	C₂×C₄×D₄	1	2	yes	—
231	C₄×C₁₃₁	D₄²	1	1	yes	characteristic
232	C₄×C₁₃₁	#551	1	1	yes	characteristic
233	C₂×C₁₃₁	—	2	2	no	—
234	C₂×C₁₃₁	—	2	1	no	—
235	C₂×C₁₃₁	—	4	4	no	—
236	C₂×C₁₃₁	—	8	1	no	—
237	C₂×C₁₃₁	—	8	1	no	—
238	C₂×C₁₃₁	#2358	1	1	yes	characteristic
239	#22899	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₁₃₁	#22899	1	1	yes	characteristic, direct product factor, Sylow
241	#3018	C₂×C₁₃₁	1	1	yes	characteristic
242	#2956	C₂×C₁₃₁	1	2	yes	complemented
243	#2901	C₂×C₁₃₁	1	2	yes	complemented
244	#1962	C₂×C₁₃₁	1	1	yes	characteristic, complemented
245	#1932	C₂×C₁₃₁	1	2	yes	complemented
246	#1906	C₂×C₁₃₁	1	2	yes	complemented
247	#1884	C₂×C₁₃₁	1	1	yes	characteristic, complemented
248	#1861	C₂×C₁₃₁	1	2	yes	complemented
249	C₄×#104	C₂×C₁₃₁	1	2	yes	complemented
250	#585	C₂²×C₁₃₁	1	1	yes	characteristic
251	#575	C₂²×C₁₃₁	1	2	yes	—
252	#568	C₂²×C₁₃₁	1	2	yes	—
253	#568	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
254	#532	C₂²×C₁₃₁	1	1	yes	characteristic
255	C₄×#41	C₂²×C₁₃₁	1	2	yes	—
256	#456	C₄×C₁₃₁	1	2	yes	complemented
257	#455	C₄×C₁₃₁	1	2	yes	complemented
258	#454	C₄×C₁₃₁	1	2	yes	complemented
259	#453	C₄×C₁₃₁	1	2	yes	complemented
260	#444	—	2	4	no	—
261	#443	—	2	4	no	—
262	#430	C₂²×C₁₃₁	1	2	yes	complemented
263	#423	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
264	#421	—	2	4	no	—
265	#421	C₂²×C₁₃₁	1	2	yes	—
266	#421	C₂²×C₁₃₁	1	2	yes	—
267	C₂×#104	—	2	4	no	—
268	C₂×#104	C₂²×C₁₃₁	1	2	yes	—
269	C₂×#104	C₂²×C₁₃₁	1	2	yes	—
270	C₂×#104	C₂²×C₁₃₁	1	2	yes	—
271	C₂×#104	C₂²×C₁₃₁	1	2	yes	complemented
272	#413	C₂²×C₁₃₁	1	1	yes	characteristic
273	#410	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
274	C₄×M₁₆	C₂²×C₁₃₁	1	2	yes	complemented
275	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
276	#344	C₂²×C₁₃₁	1	2	yes	complemented
277	#339	C₂²×C₁₃₁	1	2	yes	complemented
278	#339	C₂²×C₁₃₁	1	2	yes	complemented
279	2₋¹⁺⁴	—	2	2	no	—
280	2₋¹⁺⁴	C₂×C₄×C₁₃₁	1	2	yes	—
281	H(5,𝔽₂)	—	2	2	no	—
282	H(5,𝔽₂)	—	4	1	no	—
283	H(5,𝔽₂)	C₂×C₄×C₁₃₁	1	2	yes	—
284	C₂×#41	—	2	4	no	—
285	C₂×#41	—	4	1	no	—
286	C₂×#41	C₂³×C₁₃₁	1	1	yes	characteristic
287	C₂×#41	C₂³×C₁₃₁	1	1	yes	characteristic
288	C₂×#41	C₂³×C₁₃₁	1	2	yes	—
289	#137	—	2	2	no	—
290	#137	C₂×C₄×C₁₃₁	1	4	yes	complemented
291	AGL(1,ℤ/8)	—	2	2	no	—
292	AGL(1,ℤ/8)	C₂×C₄×C₁₃₁	1	4	yes	complemented
293	#135	—	2	4	no	—
294	#131	—	2	4	no	—
295	#131	—	2	4	no	—
296	#131	—	4	2	no	—
297	C₂×M₁₆	—	2	4	no	—
298	C₂×M₁₆	—	4	1	no	—
299	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
300	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
301	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
302	C₄⋊Q₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic, complemented
303	#127	C₂×C₄×C₁₃₁	1	1	yes	characteristic, complemented
304	#124	C₂×C₄×C₁₃₁	1	1	yes	characteristic, complemented
305	#124	C₂×C₄×C₁₃₁	1	1	yes	characteristic, complemented
306	#121	—	4	1	no	—
307	C₄×Q₈	—	2	2	no	—
308	C₄×D₄	—	2	2	no	—
309	C₄×D₄	—	4	1	no	—
310	C₄×D₄	—	4	2	no	—
311	#117	—	2	2	no	—
312	#117	C₂³×C₁₃₁	1	2	yes	—
313	C₂×C₄²	—	2	2	no	—
314	C₂×C₄²	—	4	1	no	—
315	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
316	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
317	#108	—	2	4	no	—
318	C₄⋊C₈	—	4	1	no	—
319	#104	—	2	4	no	—
320	#104	—	2	4	no	—
321	#104	—	2	2	no	—
322	#104	—	2	2	no	—
323	#104	—	2	2	no	—
324	#104	—	2	2	no	—
325	#104	C₂×C₄×C₁₃₁	1	4	yes	complemented
326	#104	C₂×C₄×C₁₃₁	1	4	yes	complemented
327	#104	D₄×C₁₃₁	1	4	yes	complemented
328	#104	D₄×C₁₃₁	1	4	yes	complemented
329	#101	C₂×C₄×C₁₃₁	1	2	yes	complemented
330	#100	C₂×C₄×C₁₃₁	1	2	yes	complemented
331	#99	—	4	1	no	—
332	#97	—	2	2	no	—
333	C₄×C₈	—	2	2	no	—
334	#41	—	2	2	no	—
335	#41	—	2	2	no	—
336	#41	—	2	4	no	—
337	#41	—	2	4	no	—
338	#41	—	2	2	no	—
339	#41	—	2	2	no	—
340	#41	—	2	2	no	—
341	#41	—	2	2	no	—
342	#41	—	4	2	no	—
343	#41	—	4	2	no	—
344	#41	—	4	4	no	—
345	#41	—	4	2	no	—
346	#41	C₂²×C₄×C₁₃₁	1	4	yes	—
347	#41	C₂×D₄×C₁₃₁	1	4	yes	—
348	C₂×Q₈	—	2	4	no	—
349	C₂×Q₈	—	4	1	no	—
350	C₂×Q₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
351	C₂×Q₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
352	C₂×Q₈	#41×C₁₃₁	1	2	yes	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	4	1	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	1	no	—
360	C₂×D₄	—	4	4	no	—
361	C₂×D₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
362	C₂×D₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
363	C₂×D₄	#41×C₁₃₁	1	2	yes	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
372	Q₁₆	—	2	4	no	—
373	SD₁₆	—	2	4	no	—
374	SD₁₆	—	2	4	no	—
375	D₈	—	2	4	no	—
376	M₁₆	—	2	2	no	—
377	M₁₆	—	2	2	no	—
378	M₁₆	—	2	2	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	4	2	no	—
381	M₁₆	—	4	4	no	—
382	M₁₆	C₂²×C₄×C₁₃₁	1	4	yes	—
383	M₁₆	C₂×D₄×C₁₃₁	1	4	yes	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	4	2	no	—
388	C₂×C₈	—	4	4	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	4	1	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	4	1	no	—
394	C₂²⋊C₄	—	4	1	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	4	2	no	—
400	C₄²	—	4	4	no	—
401	C₄²	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
402	C₄²	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
403	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
404	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	4	2	no	—
409	C₂³	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
410	Q₈	—	2	2	no	—
411	Q₈	—	2	2	no	—
412	Q₈	—	2	2	no	—
413	Q₈	—	4	2	no	—
414	Q₈	C₄×D₄×C₁₃₁	1	4	yes	—
415	D₄	—	2	4	no	—
416	D₄	—	2	4	no	—
417	D₄	—	2	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	2	2	no	—
420	D₄	—	4	4	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	2	no	—
423	D₄	—	4	2	no	—
424	D₄	—	8	2	no	—
425	D₄	C₄×D₄×C₁₃₁	1	4	yes	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	8	4	no	—
445	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
446	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
447	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
448	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
449	C₈	—	2	4	no	—
450	C₈	—	2	4	no	—
451	C₈	—	4	2	no	—
452	C₂²	—	2	4	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	8	2	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	—	16	2	no	—
460	C₂²	#518×C₁₃₁	1	1	yes	characteristic
461	C₂²	#546×C₁₃₁	1	2	yes	—
462	C₄	—	2	4	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	4	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	1	no	—
467	C₄	—	4	1	no	—
468	C₄	—	4	1	no	—
469	C₄	—	8	2	no	—
470	C₄	C₂×C₄×D₄×C₁₃₁	1	2	yes	—
471	C₄	D₄²×C₁₃₁	1	1	yes	characteristic
472	C₄	#551×C₁₃₁	1	1	yes	characteristic
473	C₂	—	2	2	no	—
474	C₂	—	2	1	no	—
475	C₂	—	4	4	no	—
476	C₂	—	8	1	no	—
477	C₂	—	8	1	no	—
478	C₂	#2358×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃₁	D₄²
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
socle	C₂×C₁₃₁	#2358
prime radical	#3018×C₁₃₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃₁ ◁ C₂²×C₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2956×C₁₃₁	C₂	semidirect
3. #2901×C₁₃₁	C₂	semidirect
4. #1962×C₁₃₁	C₂	semidirect
5. #1932×C₁₃₁	C₂	semidirect
6. #1906×C₁₃₁	C₂	semidirect
7. #1884×C₁₃₁	C₂	semidirect
8. #1861×C₁₃₁	C₂	semidirect
9. C₄×#104×C₁₃₁	C₂	semidirect
13. #568×C₁₃₁	C₂²	semidirect
16. #456×C₁₃₁	C₄	semidirect
17. #455×C₁₃₁	C₄	semidirect
18. #454×C₁₃₁	C₄	semidirect
19. #453×C₁₃₁	C₄	semidirect
22. #430×C₁₃₁	C₂²	semidirect
23. #423×C₁₃₁	C₂²	semidirect
31. C₂×#104×C₁₃₁	C₂²	semidirect
33. #410×C₁₃₁	C₂²	semidirect
34. C₄×M₁₆×C₁₃₁	C₂²	semidirect
35. C₄³×C₁₃₁	C₂²	semidirect
36. #344×C₁₃₁	C₂²	semidirect
37. #339×C₁₃₁	C₂²	semidirect
38. #339×C₁₃₁	C₂²	semidirect
50. #137×C₁₃₁	C₂×C₄	semidirect
52. AGL(1,ℤ/8)×C₁₃₁	C₂×C₄	semidirect
62. C₄⋊Q₈×C₁₃₁	C₂×C₄	semidirect
63. #127×C₁₃₁	C₂×C₄	semidirect
64. #124×C₁₃₁	C₂×C₄	semidirect
65. #124×C₁₃₁	C₂×C₄	semidirect
85. #104×C₁₃₁	C₂×C₄	semidirect
86. #104×C₁₃₁	C₂×C₄	semidirect
87. #104×C₁₃₁	D₄	semidirect
88. #104×C₁₃₁	D₄	semidirect
89. #101×C₁₃₁	C₂×C₄	semidirect
90. #100×C₁₃₁	C₂×C₄	semidirect
239. #22899	C₁₃₁	direct (N × H)
240. C₁₃₁	#22899	direct (N × H)
242. #2956	C₂×C₁₃₁	semidirect
243. #2901	C₂×C₁₃₁	semidirect
244. #1962	C₂×C₁₃₁	semidirect
245. #1932	C₂×C₁₃₁	semidirect
246. #1906	C₂×C₁₃₁	semidirect
247. #1884	C₂×C₁₃₁	semidirect
248. #1861	C₂×C₁₃₁	semidirect
249. C₄×#104	C₂×C₁₃₁	semidirect
253. #568	C₂²×C₁₃₁	semidirect
256. #456	C₄×C₁₃₁	semidirect
257. #455	C₄×C₁₃₁	semidirect
258. #454	C₄×C₁₃₁	semidirect
259. #453	C₄×C₁₃₁	semidirect
262. #430	C₂²×C₁₃₁	semidirect
263. #423	C₂²×C₁₃₁	semidirect
271. C₂×#104	C₂²×C₁₃₁	semidirect
273. #410	C₂²×C₁₃₁	semidirect
274. C₄×M₁₆	C₂²×C₁₃₁	semidirect
275. C₄³	C₂²×C₁₃₁	semidirect
276. #344	C₂²×C₁₃₁	semidirect
277. #339	C₂²×C₁₃₁	semidirect
278. #339	C₂²×C₁₃₁	semidirect
290. #137	C₂×C₄×C₁₃₁	semidirect
292. AGL(1,ℤ/8)	C₂×C₄×C₁₃₁	semidirect
302. C₄⋊Q₈	C₂×C₄×C₁₃₁	semidirect
303. #127	C₂×C₄×C₁₃₁	semidirect
304. #124	C₂×C₄×C₁₃₁	semidirect
305. #124	C₂×C₄×C₁₃₁	semidirect
325. #104	C₂×C₄×C₁₃₁	semidirect
326. #104	C₂×C₄×C₁₃₁	semidirect
327. #104	D₄×C₁₃₁	semidirect
328. #104	D₄×C₁₃₁	semidirect
329. #101	C₂×C₄×C₁₃₁	semidirect
330. #100	C₂×C₄×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3018×C₁₃₁	2
#2956×C₁₃₁	2
#2901×C₁₃₁	2
#1962×C₁₃₁	2
#1932×C₁₃₁	2
#1906×C₁₃₁	2
#1884×C₁₃₁	2
#1861×C₁₃₁	2
C₄×#104×C₁₃₁	2
#22899	131

Subgroups — C131×#22899 #45708783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#22899 #45708783