Subgroups — #577×D₁₃₁ #30680715

Order 16768.

1460 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	2₋¹⁺⁴×D₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	H(5,𝔽₂)×D₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#22554124	C₂	1	1	yes	maximal, characteristic, complemented
4	#22554123	C₂	1	1	yes	maximal, characteristic, complemented
5	#22554122	C₂	1	3	yes	maximal, complemented
6	#22554121	C₂	1	3	yes	maximal, complemented
7	#22554120	C₂	1	1	yes	maximal, characteristic, complemented
8	#22554119	C₂	1	3	yes	maximal, complemented
9	#22554118	C₂	1	3	yes	maximal, complemented
10	#137×D₁₃₁	C₂	1	3	yes	maximal, complemented
11	AGL(1,ℤ/8)×D₁₃₁	C₂	1	3	yes	maximal, complemented
12	#135×D₁₃₁	C₂	1	3	yes	maximal, complemented
13	C₂×SD₁₆×D₁₃₁	C₂	1	3	yes	maximal, complemented
14	#131×D₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#577×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	#16862294	—	2	1	no	—
17	#16862294	C₂²	1	3	yes	complemented
18	#16862293	—	2	3	no	—
19	#16862293	C₂²	1	1	yes	characteristic, complemented
20	#16862293	C₂²	1	3	yes	complemented
21	#16862292	—	2	1	no	—
22	#16862292	C₂²	1	1	yes	characteristic, complemented
23	#16862292	C₂²	1	3	yes	complemented
24	#16862291	—	2	3	no	—
25	#16862291	C₂²	1	3	yes	complemented
26	#41×D₁₃₁	—	2	1	no	—
27	#41×D₁₃₁	—	2	3	no	—
28	#41×D₁₃₁	C₂²	1	3	yes	—
29	#41×D₁₃₁	C₂²	1	1	yes	characteristic
30	#41×D₁₃₁	C₂²	1	3	yes	complemented
31	C₂×Q₈×D₁₃₁	—	2	1	no	—
32	C₂×Q₈×D₁₃₁	C₂²	1	3	yes	complemented
33	C₂×D₄×D₁₃₁	—	2	3	no	—
34	C₂×D₄×D₁₃₁	C₂²	1	3	yes	—
35	#16862279	C₂²	1	3	yes	complemented
36	#16862278	C₂²	1	6	yes	complemented
37	#16862277	C₂²	1	3	yes	complemented
38	#16862276	C₂²	1	3	yes	complemented
39	#16862275	C₂²	1	6	yes	complemented
40	#16862274	C₂²	1	3	yes	complemented
41	#16862273	C₂²	1	6	yes	complemented
42	#16862272	C₂²	1	3	yes	complemented
43	#16862271	C₂²	1	3	yes	complemented
44	#16862270	C₂²	1	6	yes	complemented
45	#16862269	C₂²	1	3	yes	complemented
46	#16862268	C₂²	1	3	yes	complemented
47	#16862267	C₂²	1	3	yes	complemented
48	#16862267	C₂²	1	3	yes	complemented
49	#16862266	C₂²	1	3	yes	complemented
50	#16862266	C₂²	1	3	yes	complemented
51	#16862265	C₂²	1	3	yes	complemented
52	Q₁₆×D₁₃₁	C₂²	1	3	yes	complemented
53	C₂×#14523502	C₂²	1	3	yes	complemented
54	C₂×#14523501	C₂²	1	3	yes	complemented
55	C₂×#14523500	C₂²	1	3	yes	complemented
56	SD₁₆×D₁₃₁	C₂²	1	3	yes	complemented
57	SD₁₆×D₁₃₁	C₂²	1	6	yes	complemented
58	SD₁₆×D₁₃₁	C₂²	1	1	yes	characteristic, complemented
59	SD₁₆×D₁₃₁	C₂²	1	6	yes	complemented
60	SD₁₆×D₁₃₁	C₂²	1	6	yes	complemented
61	D₈×D₁₃₁	C₂²	1	3	yes	complemented
62	#16862254	C₂²	1	3	yes	complemented
63	#16862253	C₂²	1	1	yes	characteristic, complemented
64	#16862252	C₂²	1	3	yes	complemented
65	M₁₆×D₁₃₁	C₂²	1	3	yes	complemented
66	C₂×C₈×D₁₃₁	C₂²	1	3	yes	complemented
67	2₋¹⁺⁴×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
68	H(5,𝔽₂)×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
69	#137×C₁₃₁	C₂²	1	3	yes	complemented
70	AGL(1,ℤ/8)×C₁₃₁	C₂²	1	3	yes	complemented
71	#135×C₁₃₁	C₂²	1	3	yes	complemented
72	C₂×SD₁₆×C₁₃₁	C₂²	1	3	yes	complemented
73	#131×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
74	C₂³×D₁₃₁	—	2	3	no	—
75	#14523514	—	2	3	no	—
76	#14523514	—	2	1	no	—
77	#14523514	D₄	1	1	yes	characteristic
78	#14523514	C₂³	1	3	yes	—
79	#14523514	C₂³	1	3	yes	complemented
80	#14523513	—	2	3	no	—
81	#14523513	—	2	3	no	—
82	#14523513	—	2	6	no	—
83	#14523513	—	2	3	no	—
84	#14523513	—	2	3	no	—
85	#14523513	C₂³	1	3	yes	—
86	#14523513	C₂³	1	3	yes	—
87	#14523513	C₂³	1	3	yes	complemented
88	#14523512	—	2	3	no	—
89	#14523512	—	2	6	no	—
90	#14523512	—	2	3	no	—
91	#14523512	—	2	3	no	—
92	#14523512	—	2	3	no	—
93	#14523512	D₄	1	3	yes	—
94	#14523512	C₂³	1	3	yes	—
95	#14523512	C₂³	1	3	yes	complemented
96	C₂×Dic₂₆₂	—	2	3	no	—
97	C₂×Dic₂₆₂	—	2	3	no	—
98	C₂×Dic₂₆₂	C₂³	1	3	yes	complemented
99	Q₈×D₁₃₁	—	2	3	no	—
100	Q₈×D₁₃₁	—	2	3	no	—
101	Q₈×D₁₃₁	—	2	3	no	—
102	Q₈×D₁₃₁	—	2	1	no	—
103	Q₈×D₁₃₁	D₄	1	1	yes	characteristic
104	Q₈×D₁₃₁	C₂³	1	3	yes	—
105	Q₈×D₁₃₁	C₂³	1	1	yes	characteristic
106	Q₈×D₁₃₁	C₂³	1	6	yes	complemented
107	C₂×D₅₂₄	—	2	3	no	—
108	C₂×D₅₂₄	C₂³	1	3	yes	—
109	C₂×C₂²⋊D₁₃₁	—	2	6	no	—
110	C₂×C₂²⋊D₁₃₁	—	2	3	no	—
111	D₄×D₁₃₁	—	2	3	no	—
112	D₄×D₁₃₁	—	2	3	no	—
113	D₄×D₁₃₁	—	2	3	no	—
114	D₄×D₁₃₁	—	2	6	no	—
115	D₄×D₁₃₁	—	2	3	no	—
116	D₄×D₁₃₁	—	2	3	no	—
117	D₄×D₁₃₁	—	2	3	no	—
118	D₄×D₁₃₁	D₄	1	3	yes	—
119	D₄×D₁₃₁	C₂³	1	1	yes	characteristic
120	D₄×D₁₃₁	C₂³	1	3	yes	—
121	D₄×D₁₃₁	C₂³	1	6	yes	—
122	C₂×C₄×D₁₃₁	—	2	3	no	—
123	C₂×C₄×D₁₃₁	—	2	3	no	—
124	C₂×C₄×D₁₃₁	—	2	3	no	—
125	C₂×C₄×D₁₃₁	C₂³	1	3	yes	—
126	Dic₅₂₄	C₂³	1	3	yes	complemented
127	#14523503	C₂³	1	3	yes	complemented
128	#14523503	C₂³	1	3	yes	complemented
129	#14523502	C₂³	1	3	yes	complemented
130	#14523502	C₂³	1	6	yes	complemented
131	#14523502	C₂³	1	1	yes	characteristic, complemented
132	#14523501	C₂³	1	3	yes	complemented
133	#14523501	C₂³	1	6	yes	complemented
134	#14523501	C₂³	1	1	yes	characteristic, complemented
135	#14523500	C₂³	1	3	yes	complemented
136	#14523500	C₂³	1	6	yes	complemented
137	#14523500	C₂³	1	1	yes	characteristic, complemented
138	D₁₀₄₈	C₂³	1	3	yes	complemented
139	#14523498	C₂³	1	3	yes	complemented
140	#14523498	C₂³	1	3	yes	complemented
141	#14523497	C₂³	1	3	yes	complemented
142	#14523496	C₂³	1	6	yes	complemented
143	C₂×C₁₃₁⋊C₈	C₂³	1	3	yes	complemented
144	C₈×D₁₃₁	C₂³	1	1	yes	characteristic
145	C₈×D₁₃₁	C₂³	1	3	yes	—
146	C₈×D₁₃₁	C₂³	1	3	yes	complemented
147	C₈×D₁₃₁	C₂³	1	3	yes	complemented
148	#41×C₁₃₁	—	2	1	no	—
149	#41×C₁₃₁	—	2	3	no	—
150	#41×C₁₃₁	C₂³	1	3	yes	—
151	#41×C₁₃₁	C₂³	1	1	yes	characteristic
152	#41×C₁₃₁	C₂³	1	3	yes	complemented
153	C₂×Q₈×C₁₃₁	—	2	1	no	—
154	C₂×Q₈×C₁₃₁	C₂³	1	3	yes	complemented
155	C₂×D₄×C₁₃₁	—	2	3	no	—
156	C₂×D₄×C₁₃₁	C₂³	1	3	yes	—
157	Q₁₆×C₁₃₁	C₂³	1	3	yes	complemented
158	SD₁₆×C₁₃₁	C₂³	1	3	yes	complemented
159	SD₁₆×C₁₃₁	C₂³	1	6	yes	complemented
160	SD₁₆×C₁₃₁	C₂³	1	1	yes	characteristic, complemented
161	D₈×C₁₃₁	C₂³	1	3	yes	complemented
162	M₁₆×C₁₃₁	C₂³	1	3	yes	complemented
163	C₂×C₈×C₁₃₁	C₂³	1	3	yes	complemented
164	C₂²×D₁₃₁	—	2	3	no	—
165	C₂²×D₁₃₁	—	2	1	no	—
166	C₂²×D₁₃₁	—	2	3	no	—
167	C₂²×D₁₃₁	—	2	6	no	—
168	C₂²×D₁₃₁	—	8	6	no	—
169	C₂²×D₁₃₁	C₂×D₄	1	3	yes	—
170	Dic₂₆₂	—	2	3	no	—
171	Dic₂₆₂	—	2	3	no	—
172	Dic₂₆₂	—	2	6	no	—
173	Dic₂₆₂	—	2	1	no	—
174	Dic₂₆₂	C₂×D₄	1	3	yes	—
175	Dic₂₆₂	C₂⁴	1	3	yes	—
176	Dic₂₆₂	C₂⁴	1	1	yes	characteristic
177	D₅₂₄	—	2	3	no	—
178	D₅₂₄	—	2	3	no	—
179	D₅₂₄	—	2	3	no	—
180	D₅₂₄	C₂×D₄	1	3	yes	—
181	D₅₂₄	C₂⁴	1	1	yes	characteristic
182	D₅₂₄	C₂⁴	1	3	yes	—
183	C₂²⋊D₁₃₁	—	2	3	no	—
184	C₂²⋊D₁₃₁	—	2	3	no	—
185	C₂²⋊D₁₃₁	—	2	3	no	—
186	C₂²⋊D₁₃₁	—	2	3	no	—
187	C₂²⋊D₁₃₁	—	2	6	no	—
188	C₂²⋊D₁₃₁	—	2	3	no	—
189	C₂²⋊D₁₃₁	—	2	1	no	—
190	C₂²⋊D₁₃₁	C₂×D₄	1	6	yes	—
191	C₂×Dic₁₃₁	—	2	3	no	—
192	C₂×Dic₁₃₁	—	2	3	no	—
193	C₂×Dic₁₃₁	—	2	3	no	—
194	C₂×Dic₁₃₁	C₂×D₄	1	3	yes	—
195	C₄×D₁₃₁	—	2	1	no	—
196	C₄×D₁₃₁	—	2	3	no	—
197	C₄×D₁₃₁	—	2	6	no	—
198	C₄×D₁₃₁	—	2	3	no	—
199	C₄×D₁₃₁	—	2	3	no	—
200	C₄×D₁₃₁	—	2	3	no	—
201	C₄×D₁₃₁	—	2	3	no	—
202	C₄×D₁₃₁	C₂×D₄	1	3	yes	—
203	C₄×D₁₃₁	C₂×D₄	1	3	yes	—
204	C₄×D₁₃₁	C₂⁴	1	1	yes	characteristic
205	C₄×D₁₃₁	C₂⁴	1	3	yes	—
206	C₁₃₁⋊C₈	C₂⁴	1	1	yes	characteristic
207	C₁₃₁⋊C₈	C₂⁴	1	3	yes	—
208	C₂³×C₁₃₁	—	2	3	no	—
209	Q₈×C₁₃₁	—	2	3	no	—
210	Q₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
211	Q₈×C₁₃₁	C₂⁴	1	3	yes	—
212	Q₈×C₁₃₁	C₂⁴	1	1	yes	characteristic
213	D₄×C₁₃₁	—	2	3	no	—
214	D₄×C₁₃₁	—	2	3	no	—
215	D₄×C₁₃₁	—	2	3	no	—
216	D₄×C₁₃₁	C₂×D₄	1	3	yes	—
217	D₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
218	D₄×C₁₃₁	C₂⁴	1	3	yes	—
219	C₂×C₄×C₁₃₁	—	2	3	no	—
220	C₂×C₄×C₁₃₁	—	2	3	no	—
221	C₂×C₄×C₁₃₁	—	2	3	no	—
222	C₂×C₄×C₁₃₁	C₂⁴	1	3	yes	—
223	C₈×C₁₃₁	C₂⁴	1	1	yes	characteristic
224	C₈×C₁₃₁	C₂⁴	1	3	yes	—
225	C₂²×C₁₃₁	—	2	1	no	—
226	C₂²×C₁₃₁	—	2	3	no	—
227	C₂²×C₁₃₁	—	8	3	no	—
228	C₂²×C₁₃₁	C₂²×D₄	1	3	yes	—
229	C₂×D₁₃₁	—	2	6	no	—
230	C₂×D₁₃₁	—	2	1	no	—
231	C₂×D₁₃₁	—	2	3	no	—
232	C₂×D₁₃₁	—	4	2	no	—
233	C₂×D₁₃₁	—	4	6	no	—
234	C₂×D₁₃₁	—	8	6	no	—
235	C₂×D₁₃₁	—	8	3	no	—
236	C₂×D₁₃₁	C₂²×D₄	1	3	yes	—
237	C₂×D₁₃₁	C₂²×D₄	1	1	yes	characteristic
238	C₄×C₁₃₁	—	2	1	no	—
239	C₄×C₁₃₁	—	2	3	no	—
240	C₄×C₁₃₁	C₂²×D₄	1	3	yes	—
241	C₄×C₁₃₁	C₂⁵	1	1	yes	characteristic
242	Dic₁₃₁	—	2	1	no	—
243	Dic₁₃₁	—	2	3	no	—
244	Dic₁₃₁	C₂²×D₄	1	3	yes	—
245	Dic₁₃₁	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₁₃₁	—	2	3	no	—
247	C₂×C₁₃₁	—	4	3	no	—
248	C₂×C₁₃₁	—	4	1	no	—
249	C₂×C₁₃₁	C₂³×D₄	1	1	yes	characteristic
250	D₁₃₁	—	2	3	no	—
251	D₁₃₁	—	4	1	no	—
252	D₁₃₁	—	4	3	no	—
253	D₁₃₁	#577	1	2	yes	direct product factor
254	C₁₃₁	C₂×#577	1	1	yes	characteristic, complemented, Sylow
255	C₂×#577	—	131	1	no	maximal, Sylow
256	C₂×2₋¹⁺⁴	—	131	1	no	—
257	C₂×H(5,𝔽₂)	—	131	1	no	—
258	#577	—	131	1	no	—
259	#577	—	131	1	no	—
260	#577	—	131	3	no	—
261	#577	—	131	3	no	—
262	#577	—	131	3	no	—
263	#577	—	131	3	no	—
264	#577	—	131	1	no	—
265	#577	D₁₃₁	1	1	yes	characteristic, direct product factor
266	C₂×#137	—	131	3	no	—
267	C₂×AGL(1,ℤ/8)	—	131	3	no	—
268	C₂×#135	—	131	3	no	—
269	C₂²×SD₁₆	—	131	3	no	—
270	C₂×#131	—	131	1	no	—
271	2₋¹⁺⁴	—	262	1	no	—
272	2₋¹⁺⁴	—	262	3	no	—
273	2₋¹⁺⁴	—	131	1	no	—
274	2₋¹⁺⁴	—	131	3	no	—
275	2₋¹⁺⁴	—	131	3	no	—
276	2₋¹⁺⁴	C₂×D₁₃₁	1	1	yes	characteristic, complemented
277	H(5,𝔽₂)	—	262	3	no	—
278	H(5,𝔽₂)	—	262	1	no	—
279	H(5,𝔽₂)	—	131	3	no	—
280	H(5,𝔽₂)	—	131	1	no	—
281	H(5,𝔽₂)	—	131	3	no	—
282	H(5,𝔽₂)	C₂×D₁₃₁	1	1	yes	characteristic, complemented
283	C₂×#41	—	262	1	no	—
284	C₂×#41	—	262	3	no	—
285	C₂×#41	—	131	3	no	—
286	C₂×#41	—	131	3	no	—
287	C₂×#41	—	131	1	no	—
288	C₂²×Q₈	—	262	1	no	—
289	C₂²×Q₈	—	131	3	no	—
290	C₂²×D₄	—	262	3	no	—
291	C₂²×D₄	—	131	3	no	—
292	#137	—	131	3	no	—
293	#137	—	131	3	no	—
294	#137	—	131	6	no	—
295	#137	—	131	6	no	—
296	#137	—	131	3	no	—
297	#137	C₂×D₁₃₁	1	3	yes	complemented
298	AGL(1,ℤ/8)	—	131	3	no	—
299	AGL(1,ℤ/8)	—	131	3	no	—
300	AGL(1,ℤ/8)	—	131	6	no	—
301	AGL(1,ℤ/8)	—	131	6	no	—
302	AGL(1,ℤ/8)	—	131	3	no	—
303	AGL(1,ℤ/8)	C₂×D₁₃₁	1	3	yes	complemented
304	#135	—	131	3	no	—
305	#135	—	131	3	no	—
306	#135	—	131	3	no	—
307	#135	—	131	3	no	—
308	#135	—	131	3	no	—
309	#135	—	131	3	no	—
310	#135	—	131	3	no	—
311	#135	C₂×D₁₃₁	1	3	yes	complemented
312	C₂×Q₁₆	—	131	3	no	—
313	C₂×SD₁₆	—	131	3	no	—
314	C₂×SD₁₆	—	131	3	no	—
315	C₂×SD₁₆	—	131	3	no	—
316	C₂×SD₁₆	—	131	6	no	—
317	C₂×SD₁₆	—	131	6	no	—
318	C₂×SD₁₆	—	131	6	no	—
319	C₂×SD₁₆	—	131	1	no	—
320	C₂×SD₁₆	—	131	3	no	—
321	C₂×SD₁₆	C₂×D₁₃₁	1	3	yes	complemented
322	C₂×D₈	—	131	3	no	—
323	#131	—	131	1	no	—
324	#131	—	131	3	no	—
325	#131	—	131	3	no	—
326	#131	C₂×D₁₃₁	1	1	yes	characteristic, complemented
327	C₂×M₁₆	—	131	3	no	—
328	C₂²×C₈	—	131	3	no	—
329	C₂⁴	—	262	3	no	—
330	#41	—	2	1	no	—
331	#41	—	2	3	no	—
332	#41	—	262	3	no	—
333	#41	—	262	6	no	—
334	#41	—	262	3	no	—
335	#41	—	262	3	no	—
336	#41	—	262	3	no	—
337	#41	—	262	3	no	—
338	#41	—	262	6	no	—
339	#41	—	262	1	no	—
340	#41	—	262	3	no	—
341	#41	—	262	3	no	—
342	#41	—	262	3	no	—
343	#41	—	262	3	no	—
344	#41	—	131	3	no	—
345	#41	—	131	3	no	—
346	#41	—	131	3	no	—
347	#41	—	131	3	no	—
348	#41	—	131	3	no	—
349	#41	—	131	3	no	—
350	#41	—	131	1	no	—
351	#41	—	131	3	no	—
352	#41	—	131	3	no	—
353	#41	C₂²×D₁₃₁	1	3	yes	—
354	#41	C₂²×D₁₃₁	1	1	yes	characteristic
355	#41	C₂²×D₁₃₁	1	3	yes	complemented
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	262	3	no	—
358	C₂×Q₈	—	262	3	no	—
359	C₂×Q₈	—	262	3	no	—
360	C₂×Q₈	—	262	1	no	—
361	C₂×Q₈	—	262	3	no	—
362	C₂×Q₈	—	262	3	no	—
363	C₂×Q₈	—	131	3	no	—
364	C₂×Q₈	—	131	1	no	—
365	C₂×Q₈	—	131	6	no	—
366	C₂×Q₈	—	131	3	no	—
367	C₂×Q₈	—	131	1	no	—
368	C₂×Q₈	C₂²×D₁₃₁	1	3	yes	complemented
369	C₂×D₄	—	2	3	no	—
370	C₂×D₄	—	262	3	no	—
371	C₂×D₄	—	262	3	no	—
372	C₂×D₄	—	262	3	no	—
373	C₂×D₄	—	262	6	no	—
374	C₂×D₄	—	262	3	no	—
375	C₂×D₄	—	262	6	no	—
376	C₂×D₄	—	262	3	no	—
377	C₂×D₄	—	262	3	no	—
378	C₂×D₄	—	262	3	no	—
379	C₂×D₄	—	262	3	no	—
380	C₂×D₄	—	131	1	no	—
381	C₂×D₄	—	131	3	no	—
382	C₂×D₄	—	131	6	no	—
383	C₂×D₄	—	131	3	no	—
384	C₂×D₄	—	131	3	no	—
385	C₂×D₄	C₂²×D₁₃₁	1	3	yes	—
386	C₂²×C₄	—	262	3	no	—
387	C₂²×C₄	—	262	3	no	—
388	C₂²×C₄	—	262	3	no	—
389	C₂²×C₄	—	131	3	no	—
390	Q₁₆	—	131	3	no	—
391	Q₁₆	—	131	3	no	—
392	Q₁₆	—	131	3	no	—
393	Q₁₆	C₂²×D₁₃₁	1	3	yes	complemented
394	SD₁₆	—	131	3	no	—
395	SD₁₆	—	131	6	no	—
396	SD₁₆	—	131	1	no	—
397	SD₁₆	—	131	3	no	—
398	SD₁₆	—	131	6	no	—
399	SD₁₆	—	131	1	no	—
400	SD₁₆	—	131	3	no	—
401	SD₁₆	—	131	6	no	—
402	SD₁₆	—	131	1	no	—
403	SD₁₆	C₂²×D₁₃₁	1	3	yes	complemented
404	SD₁₆	C₂²×D₁₃₁	1	6	yes	complemented
405	SD₁₆	C₂²×D₁₃₁	1	1	yes	characteristic, complemented
406	D₈	—	131	3	no	—
407	D₈	—	131	3	no	—
408	D₈	—	131	3	no	—
409	D₈	C₂²×D₁₃₁	1	3	yes	complemented
410	M₁₆	—	131	3	no	—
411	M₁₆	—	131	6	no	—
412	M₁₆	C₂²×D₁₃₁	1	3	yes	complemented
413	C₂×C₈	—	131	3	no	—
414	C₂×C₈	—	131	1	no	—
415	C₂×C₈	—	131	3	no	—
416	C₂×C₈	—	131	3	no	—
417	C₂×C₈	—	131	3	no	—
418	C₂×C₈	C₂²×D₁₃₁	1	3	yes	complemented
419	C₂³	—	2	3	no	—
420	C₂³	—	262	1	no	—
421	C₂³	—	262	3	no	—
422	C₂³	—	262	6	no	—
423	C₂³	—	262	3	no	—
424	C₂³	—	1048	6	no	—
425	C₂³	—	131	3	no	—
426	Q₈	—	2	3	no	—
427	Q₈	—	262	6	no	—
428	Q₈	—	262	3	no	—
429	Q₈	—	262	1	no	—
430	Q₈	—	262	3	no	—
431	Q₈	—	131	3	no	—
432	Q₈	—	131	1	no	—
433	Q₈	—	131	3	no	—
434	Q₈	D₄×D₁₃₁	1	1	yes	characteristic
435	Q₈	C₂³×D₁₃₁	1	3	yes	—
436	Q₈	C₂³×D₁₃₁	1	1	yes	characteristic
437	D₄	—	2	3	no	—
438	D₄	—	2	3	no	—
439	D₄	—	2	3	no	—
440	D₄	—	262	3	no	—
441	D₄	—	262	3	no	—
442	D₄	—	262	3	no	—
443	D₄	—	262	3	no	—
444	D₄	—	262	3	no	—
445	D₄	—	262	3	no	—
446	D₄	—	262	6	no	—
447	D₄	—	262	3	no	—
448	D₄	—	262	1	no	—
449	D₄	—	262	3	no	—
450	D₄	—	131	6	no	—
451	D₄	—	131	3	no	—
452	D₄	—	131	1	no	—
453	D₄	—	131	3	no	—
454	D₄	D₄×D₁₃₁	1	3	yes	—
455	D₄	C₂³×D₁₃₁	1	1	yes	characteristic
456	D₄	C₂³×D₁₃₁	1	3	yes	—
457	C₂×C₄	—	2	3	no	—
458	C₂×C₄	—	2	3	no	—
459	C₂×C₄	—	2	3	no	—
460	C₂×C₄	—	262	1	no	—
461	C₂×C₄	—	262	3	no	—
462	C₂×C₄	—	262	6	no	—
463	C₂×C₄	—	262	3	no	—
464	C₂×C₄	—	262	3	no	—
465	C₂×C₄	—	262	3	no	—
466	C₂×C₄	—	262	3	no	—
467	C₂×C₄	—	262	3	no	—
468	C₂×C₄	—	262	3	no	—
469	C₂×C₄	—	262	3	no	—
470	C₂×C₄	—	131	3	no	—
471	C₂×C₄	—	131	3	no	—
472	C₂×C₄	—	131	3	no	—
473	C₂×C₄	—	131	1	no	—
474	C₂×C₄	—	131	3	no	—
475	C₂×C₄	C₂³×D₁₃₁	1	3	yes	—
476	C₈	—	131	1	no	—
477	C₈	—	131	3	no	—
478	C₈	C₂³×D₁₃₁	1	1	yes	characteristic
479	C₈	C₂³×D₁₃₁	1	3	yes	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	3	no	—
482	C₂²	—	262	6	no	—
483	C₂²	—	262	1	no	—
484	C₂²	—	262	3	no	—
485	C₂²	—	8	3	no	—
486	C₂²	—	524	6	no	—
487	C₂²	—	524	2	no	—
488	C₂²	—	1048	3	no	—
489	C₂²	—	1048	6	no	—
490	C₂²	—	131	3	no	—
491	C₂²	—	131	1	no	—
492	C₂²	C₂×D₄×D₁₃₁	1	3	yes	—
493	C₄	—	2	1	no	—
494	C₄	—	2	3	no	—
495	C₄	—	262	1	no	—
496	C₄	—	262	3	no	—
497	C₄	—	131	3	no	—
498	C₄	—	131	1	no	—
499	C₄	C₂×D₄×D₁₃₁	1	3	yes	—
500	C₄	C₂⁴×D₁₃₁	1	1	yes	characteristic
501	C₂	—	2	3	no	—
502	C₂	—	4	3	no	—
503	C₂	—	4	1	no	—
504	C₂	—	262	3	no	—
505	C₂	—	524	3	no	—
506	C₂	—	524	1	no	—
507	C₂	—	131	2	no	—
508	C₂	C₂²×D₄×D₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₁₃₁
commutator, cosocle	C₄×C₁₃₁	C₂⁵
Frattini	C₄	C₂⁴×D₁₃₁
Fitting	#577×C₁₃₁	C₂
socle	C₂×C₁₃₁	C₂³×D₄
hypercenter	#577	D₁₃₁
hypocenter	C₁₃₁	C₂×#577
LCS	G ▷ C₄×C₁₃₁ ▷ C₂×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₂ ◁ #41 ◁ #577

Complements

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

N	H ≅ G/N	type
1. 2₋¹⁺⁴×D₁₃₁	C₂	semidirect
2. H(5,𝔽₂)×D₁₃₁	C₂	semidirect
3. #22554124	C₂	semidirect
4. #22554123	C₂	semidirect
5. #22554122	C₂	semidirect
6. #22554121	C₂	semidirect
7. #22554120	C₂	semidirect
8. #22554119	C₂	semidirect
9. #22554118	C₂	semidirect
10. #137×D₁₃₁	C₂	semidirect
11. AGL(1,ℤ/8)×D₁₃₁	C₂	semidirect
12. #135×D₁₃₁	C₂	semidirect
13. C₂×SD₁₆×D₁₃₁	C₂	semidirect
14. #131×D₁₃₁	C₂	semidirect
15. #577×C₁₃₁	C₂	semidirect
17. #16862294	C₂²	semidirect
19. #16862293	C₂²	semidirect
20. #16862293	C₂²	semidirect
22. #16862292	C₂²	semidirect
23. #16862292	C₂²	semidirect
25. #16862291	C₂²	semidirect
30. #41×D₁₃₁	C₂²	semidirect
32. C₂×Q₈×D₁₃₁	C₂²	semidirect
35. #16862279	C₂²	semidirect
36. #16862278	C₂²	semidirect
37. #16862277	C₂²	semidirect
38. #16862276	C₂²	semidirect
39. #16862275	C₂²	semidirect
40. #16862274	C₂²	semidirect
41. #16862273	C₂²	semidirect
42. #16862272	C₂²	semidirect
43. #16862271	C₂²	semidirect
44. #16862270	C₂²	semidirect
45. #16862269	C₂²	semidirect
46. #16862268	C₂²	semidirect
47. #16862267	C₂²	semidirect
48. #16862267	C₂²	semidirect
49. #16862266	C₂²	semidirect
50. #16862266	C₂²	semidirect
51. #16862265	C₂²	semidirect
52. Q₁₆×D₁₃₁	C₂²	semidirect
53. C₂×#14523502	C₂²	semidirect
54. C₂×#14523501	C₂²	semidirect
55. C₂×#14523500	C₂²	semidirect
56. SD₁₆×D₁₃₁	C₂²	semidirect
57. SD₁₆×D₁₃₁	C₂²	semidirect
58. SD₁₆×D₁₃₁	C₂²	semidirect
59. SD₁₆×D₁₃₁	C₂²	semidirect
60. SD₁₆×D₁₃₁	C₂²	semidirect
61. D₈×D₁₃₁	C₂²	semidirect
62. #16862254	C₂²	semidirect
63. #16862253	C₂²	semidirect
64. #16862252	C₂²	semidirect
65. M₁₆×D₁₃₁	C₂²	semidirect
66. C₂×C₈×D₁₃₁	C₂²	semidirect
67. 2₋¹⁺⁴×C₁₃₁	C₂²	semidirect
68. H(5,𝔽₂)×C₁₃₁	C₂²	semidirect
69. #137×C₁₃₁	C₂²	semidirect
70. AGL(1,ℤ/8)×C₁₃₁	C₂²	semidirect
71. #135×C₁₃₁	C₂²	semidirect
72. C₂×SD₁₆×C₁₃₁	C₂²	semidirect
73. #131×C₁₃₁	C₂²	semidirect
79. #14523514	C₂³	semidirect
87. #14523513	C₂³	semidirect
95. #14523512	C₂³	semidirect
98. C₂×Dic₂₆₂	C₂³	semidirect
106. Q₈×D₁₃₁	C₂³	semidirect
126. Dic₅₂₄	C₂³	semidirect
127. #14523503	C₂³	semidirect
128. #14523503	C₂³	semidirect
129. #14523502	C₂³	semidirect
130. #14523502	C₂³	semidirect
131. #14523502	C₂³	semidirect
132. #14523501	C₂³	semidirect
133. #14523501	C₂³	semidirect
134. #14523501	C₂³	semidirect
135. #14523500	C₂³	semidirect
136. #14523500	C₂³	semidirect
137. #14523500	C₂³	semidirect
138. D₁₀₄₈	C₂³	semidirect
139. #14523498	C₂³	semidirect
140. #14523498	C₂³	semidirect
141. #14523497	C₂³	semidirect
142. #14523496	C₂³	semidirect
143. C₂×C₁₃₁⋊C₈	C₂³	semidirect
146. C₈×D₁₃₁	C₂³	semidirect
147. C₈×D₁₃₁	C₂³	semidirect
152. #41×C₁₃₁	C₂³	semidirect
154. C₂×Q₈×C₁₃₁	C₂³	semidirect
157. Q₁₆×C₁₃₁	C₂³	semidirect
158. SD₁₆×C₁₃₁	C₂³	semidirect
159. SD₁₆×C₁₃₁	C₂³	semidirect
160. SD₁₆×C₁₃₁	C₂³	semidirect
161. D₈×C₁₃₁	C₂³	semidirect
162. M₁₆×C₁₃₁	C₂³	semidirect
163. C₂×C₈×C₁₃₁	C₂³	semidirect
253. D₁₃₁	#577	direct (N × H)
254. C₁₃₁	C₂×#577	semidirect
265. #577	D₁₃₁	direct (N × H)
276. 2₋¹⁺⁴	C₂×D₁₃₁	semidirect
282. H(5,𝔽₂)	C₂×D₁₃₁	semidirect
297. #137	C₂×D₁₃₁	semidirect
303. AGL(1,ℤ/8)	C₂×D₁₃₁	semidirect
311. #135	C₂×D₁₃₁	semidirect
321. C₂×SD₁₆	C₂×D₁₃₁	semidirect
326. #131	C₂×D₁₃₁	semidirect
355. #41	C₂²×D₁₃₁	semidirect
368. C₂×Q₈	C₂²×D₁₃₁	semidirect
393. Q₁₆	C₂²×D₁₃₁	semidirect
403. SD₁₆	C₂²×D₁₃₁	semidirect
404. SD₁₆	C₂²×D₁₃₁	semidirect
405. SD₁₆	C₂²×D₁₃₁	semidirect
409. D₈	C₂²×D₁₃₁	semidirect
412. M₁₆	C₂²×D₁₃₁	semidirect
418. C₂×C₈	C₂²×D₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
2₋¹⁺⁴×D₁₃₁	2
H(5,𝔽₂)×D₁₃₁	2
#22554124	2
#22554123	2
#22554122	2
#22554121	2
#22554120	2
#22554119	2
#22554118	2
#137×D₁₃₁	2
AGL(1,ℤ/8)×D₁₃₁	2
#135×D₁₃₁	2
C₂×SD₁₆×D₁₃₁	2
#131×D₁₃₁	2
#577×C₁₃₁	2
C₂×#577	131

Subgroups — #577×D131 #30680715

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #577×D₁₃₁ #30680715