Subgroups — C₁₃₁×#24673 #45710557

Order 33536.

806 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3038×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#460×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#137×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2925×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2051×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2019×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#1977×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#1965×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1950×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1931×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#1801×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×AGL(1,ℤ/8)×C₁₃₁	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₁₃₁	C₂²	1	2	yes	—
15	C₂×#127×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₄×#41×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
18	#460×C₁₃₁	—	2	1	no	—
19	#460×C₁₃₁	—	2	1	no	—
20	#460×C₁₃₁	—	2	1	no	—
21	#460×C₁₃₁	—	2	1	no	—
22	#460×C₁₃₁	—	2	2	no	—
23	#459×C₁₃₁	—	2	1	no	—
24	#459×C₁₃₁	—	2	1	no	—
25	#441×C₁₃₁	—	2	1	no	—
26	#440×C₁₃₁	—	2	1	no	—
27	C₄×Q₁₆×C₁₃₁	—	2	1	no	—
28	C₄×SD₁₆×C₁₃₁	—	2	1	no	—
29	#433×C₁₃₁	—	2	2	no	—
30	#432×C₁₃₁	—	2	1	no	—
31	#431×C₁₃₁	—	2	1	no	—
32	C₂×#108×C₁₃₁	C₂²	1	2	yes	—
33	#428×C₁₃₁	C₂²	1	1	yes	characteristic
34	#423×C₁₃₁	C₂²	1	1	yes	characteristic
35	#423×C₁₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
37	#419×C₁₃₁	C₂²	1	1	yes	characteristic
38	#418×C₁₃₁	C₂²	1	2	yes	—
39	#417×C₁₃₁	C₂²	1	1	yes	characteristic
40	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
41	C₂×#101×C₁₃₁	C₂²	1	2	yes	—
42	C₂×#100×C₁₃₁	C₂²	1	2	yes	—
43	C₂×#100×C₁₃₁	C₂²	1	2	yes	—
44	#408×C₁₃₁	C₂²	1	2	yes	—
45	#405×C₁₃₁	C₂²	1	2	yes	—
46	C₄×M₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
47	#343×C₁₃₁	C₂²	1	2	yes	—
48	#341×C₁₃₁	C₂²	1	2	yes	—
49	C₂×#41×C₁₃₁	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₃₁	—	2	1	no	—
52	C₂²×D₄×C₁₃₁	—	2	1	no	—
53	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
54	#137×C₁₃₁	—	2	2	no	—
55	#137×C₁₃₁	—	2	2	no	—
56	AGL(1,ℤ/8)×C₁₃₁	—	4	2	no	—
57	AGL(1,ℤ/8)×C₁₃₁	—	4	2	no	—
58	C₂×Q₁₆×C₁₃₁	—	2	1	no	—
59	C₂×SD₁₆×C₁₃₁	—	2	1	no	—
60	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
61	C₂×SD₁₆×C₁₃₁	—	2	4	no	—
62	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
63	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
64	C₂×SD₁₆×C₁₃₁	—	4	2	no	—
65	C₂×D₈×C₁₃₁	—	2	2	no	—
66	C₂×M₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
68	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
69	C₂×M₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
71	#127×C₁₃₁	—	2	1	no	—
72	#127×C₁₃₁	—	2	1	no	—
73	#127×C₁₃₁	—	2	1	no	—
74	#127×C₁₃₁	—	2	1	no	—
75	C₄×Q₈×C₁₃₁	—	2	1	no	—
76	C₄×Q₈×C₁₃₁	—	2	1	no	—
77	C₄×Q₈×C₁₃₁	—	2	1	no	—
78	C₄×Q₈×C₁₃₁	—	2	1	no	—
79	C₄×Q₈×C₁₃₁	D₄	1	1	yes	characteristic
80	C₄×Q₈×C₁₃₁	D₄	1	1	yes	characteristic
81	C₄×D₄×C₁₃₁	—	2	1	no	—
82	C₄×D₄×C₁₃₁	—	2	1	no	—
83	C₄×D₄×C₁₃₁	D₄	1	1	yes	characteristic
84	C₄×D₄×C₁₃₁	D₄	1	1	yes	characteristic
85	#117×C₁₃₁	—	2	1	no	—
86	#117×C₁₃₁	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₃₁	—	2	1	no	—
90	C₂×C₄²×C₁₃₁	—	2	1	no	—
91	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
92	#108×C₁₃₁	—	4	2	no	—
93	#107×C₁₃₁	—	2	1	no	—
94	#106×C₁₃₁	—	2	1	no	—
95	C₄⋊C₈×C₁₃₁	—	2	1	no	—
96	C₄⋊C₈×C₁₃₁	—	2	1	no	—
97	C₄⋊C₈×C₁₃₁	—	2	1	no	—
98	C₄⋊C₈×C₁₃₁	—	2	1	no	—
99	C₄⋊C₈×C₁₃₁	D₄	1	1	yes	characteristic
100	C₄⋊C₈×C₁₃₁	D₄	1	1	yes	characteristic
101	C₄⋊C₈×C₁₃₁	D₄	1	2	yes	—
102	#103×C₁₃₁	—	2	1	no	—
103	#103×C₁₃₁	—	2	1	no	—
104	#103×C₁₃₁	—	2	1	no	—
105	#102×C₁₃₁	—	2	1	no	—
106	#102×C₁₃₁	—	2	2	no	—
107	#102×C₁₃₁	—	2	2	no	—
108	#102×C₁₃₁	—	2	2	no	—
109	#102×C₁₃₁	—	2	2	no	—
110	#101×C₁₃₁	—	4	2	no	—
111	#100×C₁₃₁	—	2	4	no	—
112	#100×C₁₃₁	—	4	2	no	—
113	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
114	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
115	#97×C₁₃₁	—	2	2	no	—
116	#97×C₁₃₁	—	2	1	no	—
117	C₄×C₈×C₁₃₁	—	2	2	no	—
118	C₄×C₈×C₁₃₁	—	2	1	no	—
119	C₂⁴×C₁₃₁	—	2	2	no	—
120	#41×C₁₃₁	—	2	1	no	—
121	#41×C₁₃₁	—	2	1	no	—
122	#41×C₁₃₁	—	2	1	no	—
123	#41×C₁₃₁	—	2	1	no	—
124	C₂×Q₈×C₁₃₁	—	2	1	no	—
125	C₂×Q₈×C₁₃₁	—	2	1	no	—
126	C₂×Q₈×C₁₃₁	—	2	1	no	—
127	C₂×Q₈×C₁₃₁	—	2	1	no	—
128	C₂×Q₈×C₁₃₁	—	2	1	no	—
129	C₂×Q₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
130	C₂×Q₈×C₁₃₁	#41	1	2	yes	—
131	C₂×D₄×C₁₃₁	—	2	1	no	—
132	C₂×D₄×C₁₃₁	—	2	2	no	—
133	C₂×D₄×C₁₃₁	—	2	2	no	—
134	C₂×D₄×C₁₃₁	—	2	2	no	—
135	C₂×D₄×C₁₃₁	—	2	2	no	—
136	C₂×D₄×C₁₃₁	—	2	2	no	—
137	C₂×D₄×C₁₃₁	—	2	2	no	—
138	C₂×D₄×C₁₃₁	—	4	1	no	—
139	C₂×D₄×C₁₃₁	—	4	1	no	—
140	C₂×D₄×C₁₃₁	—	4	1	no	—
141	C₂×D₄×C₁₃₁	—	4	1	no	—
142	C₂×D₄×C₁₃₁	—	8	2	no	—
143	C₂×D₄×C₁₃₁	—	8	2	no	—
144	C₂×D₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃₁	—	2	1	no	—
146	C₂²×C₄×C₁₃₁	—	2	1	no	—
147	C₂²×C₄×C₁₃₁	—	2	1	no	—
148	C₂²×C₄×C₁₃₁	—	2	1	no	—
149	C₂²×C₄×C₁₃₁	—	2	1	no	—
150	C₂²×C₄×C₁₃₁	#41	1	1	yes	characteristic
151	C₂²×C₄×C₁₃₁	#41	1	1	yes	characteristic
152	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
153	Q₁₆×C₁₃₁	—	2	4	no	—
154	SD₁₆×C₁₃₁	—	2	4	no	—
155	SD₁₆×C₁₃₁	—	4	4	no	—
156	SD₁₆×C₁₃₁	—	4	4	no	—
157	SD₁₆×C₁₃₁	—	4	4	no	—
158	D₈×C₁₃₁	—	4	4	no	—
159	M₁₆×C₁₃₁	—	2	1	no	—
160	M₁₆×C₁₃₁	—	2	2	no	—
161	M₁₆×C₁₃₁	—	2	1	no	—
162	M₁₆×C₁₃₁	—	2	2	no	—
163	M₁₆×C₁₃₁	—	2	2	no	—
164	M₁₆×C₁₃₁	—	2	1	no	—
165	M₁₆×C₁₃₁	—	2	2	no	—
166	M₁₆×C₁₃₁	#41	1	2	yes	—
167	C₂×C₈×C₁₃₁	—	2	1	no	—
168	C₂×C₈×C₁₃₁	—	2	2	no	—
169	C₂×C₈×C₁₃₁	—	2	2	no	—
170	C₂×C₈×C₁₃₁	—	2	2	no	—
171	C₂×C₈×C₁₃₁	—	2	1	no	—
172	C₂×C₈×C₁₃₁	—	2	2	no	—
173	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
174	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
175	C₄⋊C₄×C₁₃₁	—	2	1	no	—
176	C₄⋊C₄×C₁₃₁	—	2	1	no	—
177	C₄⋊C₄×C₁₃₁	—	2	1	no	—
178	C₄⋊C₄×C₁₃₁	—	2	1	no	—
179	C₄⋊C₄×C₁₃₁	—	4	1	no	—
180	C₄⋊C₄×C₁₃₁	—	4	1	no	—
181	C₄⋊C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
182	C₄⋊C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
183	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
184	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
185	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
186	C₄²×C₁₃₁	—	2	1	no	—
187	C₄²×C₁₃₁	—	2	1	no	—
188	C₄²×C₁₃₁	—	2	1	no	—
189	C₄²×C₁₃₁	—	4	1	no	—
190	C₄²×C₁₃₁	—	4	1	no	—
191	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
195	C₂³×C₁₃₁	—	2	1	no	—
196	C₂³×C₁₃₁	—	4	2	no	—
197	C₂³×C₁₃₁	—	4	2	no	—
198	C₂³×C₁₃₁	—	4	2	no	—
199	C₂³×C₁₃₁	—	8	2	no	—
200	C₂³×C₁₃₁	—	8	2	no	—
201	C₂³×C₁₃₁	C₂×#41	1	1	yes	characteristic
202	Q₈×C₁₃₁	—	2	2	no	—
203	Q₈×C₁₃₁	—	2	1	no	—
204	Q₈×C₁₃₁	—	2	1	no	—
205	Q₈×C₁₃₁	—	2	2	no	—
206	Q₈×C₁₃₁	—	4	1	no	—
207	Q₈×C₁₃₁	—	4	1	no	—
208	D₄×C₁₃₁	—	2	1	no	—
209	D₄×C₁₃₁	—	2	1	no	—
210	D₄×C₁₃₁	—	4	1	no	—
211	D₄×C₁₃₁	—	4	1	no	—
212	D₄×C₁₃₁	—	4	2	no	—
213	D₄×C₁₃₁	—	4	2	no	—
214	D₄×C₁₃₁	—	4	2	no	—
215	D₄×C₁₃₁	—	4	2	no	—
216	D₄×C₁₃₁	—	8	2	no	—
217	D₄×C₁₃₁	—	8	2	no	—
218	D₄×C₁₃₁	—	8	2	no	—
219	D₄×C₁₃₁	—	8	2	no	—
220	C₂×C₄×C₁₃₁	—	2	2	no	—
221	C₂×C₄×C₁₃₁	—	2	1	no	—
222	C₂×C₄×C₁₃₁	—	2	1	no	—
223	C₂×C₄×C₁₃₁	—	2	1	no	—
224	C₂×C₄×C₁₃₁	—	2	2	no	—
225	C₂×C₄×C₁₃₁	—	4	1	no	—
226	C₂×C₄×C₁₃₁	—	4	1	no	—
227	C₂×C₄×C₁₃₁	—	4	1	no	—
228	C₂×C₄×C₁₃₁	—	4	1	no	—
229	C₂×C₄×C₁₃₁	—	4	1	no	—
230	C₂×C₄×C₁₃₁	—	4	2	no	—
231	C₂×C₄×C₁₃₁	—	4	1	no	—
232	C₂×C₄×C₁₃₁	—	8	1	no	—
233	C₂×C₄×C₁₃₁	—	8	1	no	—
234	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
235	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
236	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
237	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
238	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
241	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
242	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
243	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
244	C₈×C₁₃₁	—	2	2	no	—
245	C₈×C₁₃₁	—	2	2	no	—
246	C₈×C₁₃₁	—	2	2	no	—
247	C₈×C₁₃₁	—	4	1	no	—
248	C₈×C₁₃₁	—	4	2	no	—
249	C₈×C₁₃₁	—	4	2	no	—
250	C₂²×C₁₃₁	—	2	1	no	—
251	C₂²×C₁₃₁	—	2	1	no	—
252	C₂²×C₁₃₁	—	4	1	no	—
253	C₂²×C₁₃₁	—	4	1	no	—
254	C₂²×C₁₃₁	—	4	1	no	—
255	C₂²×C₁₃₁	—	8	2	no	—
256	C₂²×C₁₃₁	—	8	2	no	—
257	C₂²×C₁₃₁	—	8	2	no	—
258	C₂²×C₁₃₁	—	16	2	no	—
259	C₂²×C₁₃₁	—	16	2	no	—
260	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
261	C₂²×C₁₃₁	#553	1	1	yes	characteristic
262	C₂²×C₁₃₁	#555	1	1	yes	characteristic
263	C₄×C₁₃₁	—	2	1	no	—
264	C₄×C₁₃₁	—	2	1	no	—
265	C₄×C₁₃₁	—	2	1	no	—
266	C₄×C₁₃₁	—	4	1	no	—
267	C₄×C₁₃₁	—	4	2	no	—
268	C₄×C₁₃₁	—	4	1	no	—
269	C₄×C₁₃₁	—	4	1	no	—
270	C₄×C₁₃₁	—	8	1	no	—
271	C₄×C₁₃₁	#471	1	2	yes	—
272	C₄×C₁₃₁	#525	1	1	yes	characteristic
273	C₄×C₁₃₁	#535	1	1	yes	characteristic
274	C₄×C₁₃₁	#546	1	1	yes	characteristic
275	C₄×C₁₃₁	#550	1	1	yes	characteristic
276	C₂×C₁₃₁	—	2	1	no	—
277	C₂×C₁₃₁	—	2	1	no	—
278	C₂×C₁₃₁	—	8	1	no	—
279	C₂×C₁₃₁	—	16	2	no	—
280	C₂×C₁₃₁	#2414	1	1	yes	characteristic
281	C₂×C₁₃₁	C₂×#471	1	1	yes	characteristic
282	C₂×C₁₃₁	#3068	1	1	yes	characteristic
283	#24673	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₁₃₁	#24673	1	1	yes	characteristic, direct product factor, Sylow
285	#3038	C₂×C₁₃₁	1	1	yes	characteristic
286	C₂×#460	C₂×C₁₃₁	1	1	yes	characteristic, complemented
287	C₄×#137	C₂×C₁₃₁	1	1	yes	characteristic, complemented
288	#2925	C₂×C₁₃₁	1	1	yes	characteristic, complemented
289	#2051	C₂×C₁₃₁	1	2	yes	complemented
290	#2019	C₂×C₁₃₁	1	2	yes	complemented
291	#1977	C₂×C₁₃₁	1	2	yes	complemented
292	#1965	C₂×C₁₃₁	1	1	yes	characteristic, complemented
293	#1950	C₂×C₁₃₁	1	1	yes	characteristic, complemented
294	#1931	C₂×C₁₃₁	1	2	yes	complemented
295	#1801	C₂×C₁₃₁	1	1	yes	characteristic, complemented
296	C₂×#137	C₂²×C₁₃₁	1	1	yes	characteristic
297	C₂×AGL(1,ℤ/8)	C₂²×C₁₃₁	1	2	yes	—
298	C₂²×SD₁₆	C₂²×C₁₃₁	1	2	yes	—
299	C₂×#127	C₂²×C₁₃₁	1	1	yes	characteristic
300	C₄×#41	C₂²×C₁₃₁	1	1	yes	characteristic
301	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
302	#460	—	2	1	no	—
303	#460	—	2	1	no	—
304	#460	—	2	1	no	—
305	#460	—	2	1	no	—
306	#460	—	2	2	no	—
307	#459	—	2	1	no	—
308	#459	—	2	1	no	—
309	#441	—	2	1	no	—
310	#440	—	2	1	no	—
311	C₄×Q₁₆	—	2	1	no	—
312	C₄×SD₁₆	—	2	1	no	—
313	#433	—	2	2	no	—
314	#432	—	2	1	no	—
315	#431	—	2	1	no	—
316	C₂×#108	C₂²×C₁₃₁	1	2	yes	—
317	#428	C₂²×C₁₃₁	1	1	yes	characteristic
318	#423	C₂²×C₁₃₁	1	1	yes	characteristic
319	#423	C₂²×C₁₃₁	1	1	yes	characteristic
320	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
321	#419	C₂²×C₁₃₁	1	1	yes	characteristic
322	#418	C₂²×C₁₃₁	1	2	yes	—
323	#417	C₂²×C₁₃₁	1	1	yes	characteristic
324	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
325	C₂×#101	C₂²×C₁₃₁	1	2	yes	—
326	C₂×#100	C₂²×C₁₃₁	1	2	yes	—
327	C₂×#100	C₂²×C₁₃₁	1	2	yes	—
328	#408	C₂²×C₁₃₁	1	2	yes	—
329	#405	C₂²×C₁₃₁	1	2	yes	—
330	C₄×M₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
331	#343	C₂²×C₁₃₁	1	2	yes	—
332	#341	C₂²×C₁₃₁	1	2	yes	—
333	C₂×#41	C₂³×C₁₃₁	1	1	yes	characteristic
334	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
335	C₂²×D₄	—	2	1	no	—
336	C₂²×D₄	—	2	1	no	—
337	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
338	#137	—	2	2	no	—
339	#137	—	2	2	no	—
340	AGL(1,ℤ/8)	—	4	2	no	—
341	AGL(1,ℤ/8)	—	4	2	no	—
342	C₂×Q₁₆	—	2	1	no	—
343	C₂×SD₁₆	—	2	1	no	—
344	C₂×SD₁₆	—	2	2	no	—
345	C₂×SD₁₆	—	2	4	no	—
346	C₂×SD₁₆	—	2	2	no	—
347	C₂×SD₁₆	—	2	2	no	—
348	C₂×SD₁₆	—	4	2	no	—
349	C₂×D₈	—	2	2	no	—
350	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
351	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
352	C₂×M₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
353	C₂×M₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
355	#127	—	2	1	no	—
356	#127	—	2	1	no	—
357	#127	—	2	1	no	—
358	#127	—	2	1	no	—
359	C₄×Q₈	—	2	1	no	—
360	C₄×Q₈	—	2	1	no	—
361	C₄×Q₈	—	2	1	no	—
362	C₄×Q₈	—	2	1	no	—
363	C₄×Q₈	D₄×C₁₃₁	1	1	yes	characteristic
364	C₄×Q₈	D₄×C₁₃₁	1	1	yes	characteristic
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	—	2	1	no	—
367	C₄×D₄	D₄×C₁₃₁	1	1	yes	characteristic
368	C₄×D₄	D₄×C₁₃₁	1	1	yes	characteristic
369	#117	—	2	1	no	—
370	#117	C₂³×C₁₃₁	1	1	yes	characteristic
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
376	#108	—	4	2	no	—
377	#107	—	2	1	no	—
378	#106	—	2	1	no	—
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	—	2	1	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	2	1	no	—
383	C₄⋊C₈	D₄×C₁₃₁	1	1	yes	characteristic
384	C₄⋊C₈	D₄×C₁₃₁	1	1	yes	characteristic
385	C₄⋊C₈	D₄×C₁₃₁	1	2	yes	—
386	#103	—	2	1	no	—
387	#103	—	2	1	no	—
388	#103	—	2	1	no	—
389	#102	—	2	1	no	—
390	#102	—	2	2	no	—
391	#102	—	2	2	no	—
392	#102	—	2	2	no	—
393	#102	—	2	2	no	—
394	#101	—	4	2	no	—
395	#100	—	2	4	no	—
396	#100	—	4	2	no	—
397	C₂²⋊C₈	—	2	2	no	—
398	C₂²⋊C₈	—	2	2	no	—
399	#97	—	2	2	no	—
400	#97	—	2	1	no	—
401	C₄×C₈	—	2	2	no	—
402	C₄×C₈	—	2	1	no	—
403	C₂⁴	—	2	2	no	—
404	#41	—	2	1	no	—
405	#41	—	2	1	no	—
406	#41	—	2	1	no	—
407	#41	—	2	1	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	—	2	1	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
414	C₂×Q₈	#41×C₁₃₁	1	2	yes	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	4	1	no	—
423	C₂×D₄	—	4	1	no	—
424	C₂×D₄	—	4	1	no	—
425	C₂×D₄	—	4	1	no	—
426	C₂×D₄	—	8	2	no	—
427	C₂×D₄	—	8	2	no	—
428	C₂×D₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	#41×C₁₃₁	1	1	yes	characteristic
435	C₂²×C₄	#41×C₁₃₁	1	1	yes	characteristic
436	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
437	Q₁₆	—	2	4	no	—
438	SD₁₆	—	2	4	no	—
439	SD₁₆	—	4	4	no	—
440	SD₁₆	—	4	4	no	—
441	SD₁₆	—	4	4	no	—
442	D₈	—	4	4	no	—
443	M₁₆	—	2	1	no	—
444	M₁₆	—	2	2	no	—
445	M₁₆	—	2	1	no	—
446	M₁₆	—	2	2	no	—
447	M₁₆	—	2	2	no	—
448	M₁₆	—	2	1	no	—
449	M₁₆	—	2	2	no	—
450	M₁₆	#41×C₁₃₁	1	2	yes	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
458	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₄⋊C₄	—	4	1	no	—
465	C₄⋊C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
466	C₄⋊C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	4	1	no	—
474	C₄²	—	4	1	no	—
475	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
476	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
477	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
478	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
479	C₂³	—	2	1	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	8	2	no	—
484	C₂³	—	8	2	no	—
485	C₂³	C₂×#41×C₁₃₁	1	1	yes	characteristic
486	Q₈	—	2	2	no	—
487	Q₈	—	2	1	no	—
488	Q₈	—	2	1	no	—
489	Q₈	—	2	2	no	—
490	Q₈	—	4	1	no	—
491	Q₈	—	4	1	no	—
492	D₄	—	2	1	no	—
493	D₄	—	2	1	no	—
494	D₄	—	4	1	no	—
495	D₄	—	4	1	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	2	no	—
499	D₄	—	4	2	no	—
500	D₄	—	8	2	no	—
501	D₄	—	8	2	no	—
502	D₄	—	8	2	no	—
503	D₄	—	8	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	8	1	no	—
517	C₂×C₄	—	8	1	no	—
518	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
519	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
520	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
521	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
524	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
525	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
526	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
527	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
528	C₈	—	2	2	no	—
529	C₈	—	2	2	no	—
530	C₈	—	2	2	no	—
531	C₈	—	4	2	no	—
532	C₈	—	4	1	no	—
533	C₈	—	4	2	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	8	2	no	—
540	C₂²	—	8	2	no	—
541	C₂²	—	8	2	no	—
542	C₂²	—	16	2	no	—
543	C₂²	—	16	2	no	—
544	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
545	C₂²	#553×C₁₃₁	1	1	yes	characteristic
546	C₂²	#555×C₁₃₁	1	1	yes	characteristic
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	2	no	—
554	C₄	—	8	1	no	—
555	C₄	#471×C₁₃₁	1	2	yes	—
556	C₄	#525×C₁₃₁	1	1	yes	characteristic
557	C₄	#535×C₁₃₁	1	1	yes	characteristic
558	C₄	#546×C₁₃₁	1	1	yes	characteristic
559	C₄	#550×C₁₃₁	1	1	yes	characteristic
560	C₂	—	2	1	no	—
561	C₂	—	2	1	no	—
562	C₂	—	8	1	no	—
563	C₂	—	16	2	no	—
564	C₂	#2414×C₁₃₁	1	1	yes	characteristic
565	C₂	C₂×#471×C₁₃₁	1	1	yes	characteristic
566	C₂	#3068×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	#3038×C₁₃₁	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂×C₄²×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#460×C₁₃₁	C₂	semidirect
3. C₄×#137×C₁₃₁	C₂	semidirect
4. #2925×C₁₃₁	C₂	semidirect
5. #2051×C₁₃₁	C₂	semidirect
6. #2019×C₁₃₁	C₂	semidirect
7. #1977×C₁₃₁	C₂	semidirect
8. #1965×C₁₃₁	C₂	semidirect
9. #1950×C₁₃₁	C₂	semidirect
10. #1931×C₁₃₁	C₂	semidirect
11. #1801×C₁₃₁	C₂	semidirect
283. #24673	C₁₃₁	direct (N × H)
284. C₁₃₁	#24673	direct (N × H)
286. C₂×#460	C₂×C₁₃₁	semidirect
287. C₄×#137	C₂×C₁₃₁	semidirect
288. #2925	C₂×C₁₃₁	semidirect
289. #2051	C₂×C₁₃₁	semidirect
290. #2019	C₂×C₁₃₁	semidirect
291. #1977	C₂×C₁₃₁	semidirect
292. #1965	C₂×C₁₃₁	semidirect
293. #1950	C₂×C₁₃₁	semidirect
294. #1931	C₂×C₁₃₁	semidirect
295. #1801	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3038×C₁₃₁	2
C₂×#460×C₁₃₁	2
C₄×#137×C₁₃₁	2
#2925×C₁₃₁	2
#2051×C₁₃₁	2
#2019×C₁₃₁	2
#1977×C₁₃₁	2
#1965×C₁₃₁	2
#1950×C₁₃₁	2
#1931×C₁₃₁	2
#1801×C₁₃₁	2
#24673	131

Subgroups — C131×#24673 #45710557

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#24673 #45710557