Subgroups — C₁₃₁×#29847 #45715731

Order 33536.

840 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#486×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#433×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2628×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2619×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	#2067×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2065×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2034×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#2033×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#1993×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1961×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1846×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×#127×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×#121×C₁₃₁	C₂²	1	2	yes	—
15	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
16	#486×C₁₃₁	—	2	4	no	—
17	#433×C₁₃₁	—	2	4	no	—
18	C₂×#107×C₁₃₁	C₂²	1	2	yes	—
19	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
23	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
24	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
25	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
30	#400×C₁₃₁	—	2	1	no	—
31	#399×C₁₃₁	—	2	1	no	—
32	#395×C₁₃₁	—	2	1	no	—
33	#394×C₁₃₁	—	2	1	no	—
34	#394×C₁₃₁	—	2	1	no	—
35	#393×C₁₃₁	—	2	1	no	—
36	#392×C₁₃₁	—	2	1	no	—
37	#392×C₁₃₁	—	2	1	no	—
38	#390×C₁₃₁	C₂²	1	2	yes	—
39	#389×C₁₃₁	C₂²	1	2	yes	—
40	#382×C₁₃₁	C₂²	1	1	yes	characteristic
41	#382×C₁₃₁	C₂²	1	1	yes	characteristic
42	#380×C₁₃₁	C₂²	1	2	yes	—
43	#340×C₁₃₁	C₂²	1	2	yes	—
44	#340×C₁₃₁	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃₁	—	2	1	no	—
46	C₂²×D₄×C₁₃₁	—	2	2	no	—
47	C₂²×D₄×C₁₃₁	—	2	1	no	—
48	C₂²×D₄×C₁₃₁	—	2	1	no	—
49	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
55	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
56	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
57	#127×C₁₃₁	—	2	2	no	—
58	#127×C₁₃₁	—	2	2	no	—
59	#121×C₁₃₁	—	4	2	no	—
60	#121×C₁₃₁	—	4	2	no	—
61	#117×C₁₃₁	—	2	2	no	—
62	#117×C₁₃₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
78	#107×C₁₃₁	—	4	2	no	—
79	#106×C₁₃₁	—	4	2	no	—
80	C₄⋊C₈×C₁₃₁	—	2	2	no	—
81	C₄⋊C₈×C₁₃₁	—	2	2	no	—
82	#102×C₁₃₁	—	2	4	no	—
83	#102×C₁₃₁	—	2	4	no	—
84	#102×C₁₃₁	—	4	2	no	—
85	#102×C₁₃₁	—	4	2	no	—
86	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
87	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
88	#97×C₁₃₁	—	2	2	no	—
89	C₄×C₈×C₁₃₁	D₄	1	4	yes	complemented
90	#95×C₁₃₁	—	2	2	no	—
91	#95×C₁₃₁	—	2	1	no	—
92	#95×C₁₃₁	—	2	1	no	—
93	#95×C₁₃₁	—	2	1	no	—
94	#95×C₁₃₁	—	2	2	no	—
95	#95×C₁₃₁	—	2	1	no	—
96	C₂⁴×C₁₃₁	—	2	2	no	—
97	C₂⁴×C₁₃₁	C₂×D₄	1	1	yes	characteristic
98	C₂×Q₈×C₁₃₁	—	4	2	no	—
99	C₂×Q₈×C₁₃₁	—	8	2	no	—
100	C₂×D₄×C₁₃₁	—	2	2	no	—
101	C₂×D₄×C₁₃₁	—	2	2	no	—
102	C₂×D₄×C₁₃₁	—	2	2	no	—
103	C₂×D₄×C₁₃₁	—	2	2	no	—
104	C₂×D₄×C₁₃₁	—	2	2	no	—
105	C₂×D₄×C₁₃₁	—	2	2	no	—
106	C₂×D₄×C₁₃₁	—	4	4	no	—
107	C₂×D₄×C₁₃₁	—	4	2	no	—
108	C₂×D₄×C₁₃₁	—	4	2	no	—
109	C₂×D₄×C₁₃₁	—	8	2	no	—
110	C₂×D₄×C₁₃₁	—	8	2	no	—
111	C₂×D₄×C₁₃₁	—	8	2	no	—
112	C₂×D₄×C₁₃₁	—	8	2	no	—
113	C₂²×C₄×C₁₃₁	—	2	1	no	—
114	C₂²×C₄×C₁₃₁	—	2	1	no	—
115	C₂²×C₄×C₁₃₁	—	2	1	no	—
116	C₂²×C₄×C₁₃₁	—	2	1	no	—
117	C₂²×C₄×C₁₃₁	—	2	1	no	—
118	C₂²×C₄×C₁₃₁	—	2	1	no	—
119	C₂²×C₄×C₁₃₁	—	2	2	no	—
120	C₂²×C₄×C₁₃₁	—	2	2	no	—
121	C₂²×C₄×C₁₃₁	—	2	2	no	—
122	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
128	C₂×C₈×C₁₃₁	—	2	1	no	—
129	C₂×C₈×C₁₃₁	—	2	1	no	—
130	C₂×C₈×C₁₃₁	—	2	1	no	—
131	C₂×C₈×C₁₃₁	—	2	1	no	—
132	C₂×C₈×C₁₃₁	—	2	1	no	—
133	C₂×C₈×C₁₃₁	—	2	1	no	—
134	C₂×C₈×C₁₃₁	—	2	1	no	—
135	C₂×C₈×C₁₃₁	—	2	1	no	—
136	C₂×C₈×C₁₃₁	—	2	1	no	—
137	C₂×C₈×C₁₃₁	—	2	1	no	—
138	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
140	C₄⋊C₄×C₁₃₁	—	2	2	no	—
141	C₄⋊C₄×C₁₃₁	—	2	2	no	—
142	C₄⋊C₄×C₁₃₁	—	2	2	no	—
143	C₄⋊C₄×C₁₃₁	—	2	2	no	—
144	C₄⋊C₄×C₁₃₁	—	2	2	no	—
145	C₄⋊C₄×C₁₃₁	—	2	2	no	—
146	C₄⋊C₄×C₁₃₁	—	2	2	no	—
147	C₄⋊C₄×C₁₃₁	—	2	2	no	—
148	C₄⋊C₄×C₁₃₁	—	4	2	no	—
149	C₄⋊C₄×C₁₃₁	—	8	2	no	—
150	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
151	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
152	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
153	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
154	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
155	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
156	C₄²×C₁₃₁	—	2	1	no	—
157	C₄²×C₁₃₁	—	2	1	no	—
158	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
159	C₄²×C₁₃₁	#41	1	2	yes	—
160	C₂³×C₁₃₁	—	2	1	no	—
161	C₂³×C₁₃₁	—	2	1	no	—
162	C₂³×C₁₃₁	—	2	1	no	—
163	C₂³×C₁₃₁	—	2	2	no	—
164	C₂³×C₁₃₁	—	2	2	no	—
165	C₂³×C₁₃₁	—	4	2	no	—
166	C₂³×C₁₃₁	—	4	2	no	—
167	C₂³×C₁₃₁	—	4	2	no	—
168	C₂³×C₁₃₁	—	4	2	no	—
169	C₂³×C₁₃₁	—	4	2	no	—
170	C₂³×C₁₃₁	—	4	2	no	—
171	C₂³×C₁₃₁	—	4	2	no	—
172	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₁₃₁	—	8	4	no	—
174	D₄×C₁₃₁	—	4	2	no	—
175	D₄×C₁₃₁	—	4	2	no	—
176	D₄×C₁₃₁	—	4	2	no	—
177	D₄×C₁₃₁	—	4	2	no	—
178	D₄×C₁₃₁	—	8	4	no	—
179	D₄×C₁₃₁	—	8	4	no	—
180	D₄×C₁₃₁	—	8	8	no	—
181	C₂×C₄×C₁₃₁	—	2	2	no	—
182	C₂×C₄×C₁₃₁	—	2	2	no	—
183	C₂×C₄×C₁₃₁	—	2	1	no	—
184	C₂×C₄×C₁₃₁	—	2	1	no	—
185	C₂×C₄×C₁₃₁	—	2	1	no	—
186	C₂×C₄×C₁₃₁	—	2	1	no	—
187	C₂×C₄×C₁₃₁	—	2	1	no	—
188	C₂×C₄×C₁₃₁	—	2	2	no	—
189	C₂×C₄×C₁₃₁	—	2	2	no	—
190	C₂×C₄×C₁₃₁	—	4	1	no	—
191	C₂×C₄×C₁₃₁	—	4	1	no	—
192	C₂×C₄×C₁₃₁	—	4	1	no	—
193	C₂×C₄×C₁₃₁	—	4	1	no	—
194	C₂×C₄×C₁₃₁	—	4	2	no	—
195	C₂×C₄×C₁₃₁	—	4	2	no	—
196	C₂×C₄×C₁₃₁	—	4	2	no	—
197	C₂×C₄×C₁₃₁	—	4	2	no	—
198	C₂×C₄×C₁₃₁	—	4	2	no	—
199	C₂×C₄×C₁₃₁	—	4	2	no	—
200	C₂×C₄×C₁₃₁	—	4	2	no	—
201	C₂×C₄×C₁₃₁	—	4	2	no	—
202	C₂×C₄×C₁₃₁	—	4	2	no	—
203	C₂×C₄×C₁₃₁	#121	1	2	yes	—
204	C₂×C₄×C₁₃₁	#121	1	2	yes	—
205	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
210	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
211	C₈×C₁₃₁	—	2	2	no	—
212	C₈×C₁₃₁	—	2	2	no	—
213	C₈×C₁₃₁	—	4	1	no	—
214	C₈×C₁₃₁	—	4	1	no	—
215	C₂²×C₁₃₁	—	4	1	no	—
216	C₂²×C₁₃₁	—	4	2	no	—
217	C₂²×C₁₃₁	—	4	2	no	—
218	C₂²×C₁₃₁	—	4	1	no	—
219	C₂²×C₁₃₁	—	4	1	no	—
220	C₂²×C₁₃₁	—	8	2	no	—
221	C₂²×C₁₃₁	—	8	2	no	—
222	C₂²×C₁₃₁	—	8	2	no	—
223	C₂²×C₁₃₁	—	8	2	no	—
224	C₂²×C₁₃₁	—	8	2	no	—
225	C₂²×C₁₃₁	—	8	2	no	—
226	C₂²×C₁₃₁	—	8	2	no	—
227	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
228	C₂²×C₁₃₁	#535	1	1	yes	characteristic
229	C₂²×C₁₃₁	#536	1	1	yes	characteristic
230	C₂²×C₁₃₁	#576	1	2	yes	—
231	C₂²×C₁₃₁	#577	1	2	yes	—
232	C₄×C₁₃₁	—	2	2	no	—
233	C₄×C₁₃₁	—	2	2	no	—
234	C₄×C₁₃₁	—	4	1	no	—
235	C₄×C₁₃₁	—	4	1	no	—
236	C₄×C₁₃₁	—	4	1	no	—
237	C₄×C₁₃₁	—	8	2	no	—
238	C₄×C₁₃₁	—	8	2	no	—
239	C₄×C₁₃₁	—	8	2	no	—
240	C₄×C₁₃₁	#537	1	1	yes	characteristic
241	C₄×C₁₃₁	#537	1	1	yes	characteristic
242	C₄×C₁₃₁	#542	1	1	yes	characteristic
243	C₄×C₁₃₁	#542	1	1	yes	characteristic
244	C₂×C₁₃₁	—	8	1	no	—
245	C₂×C₁₃₁	—	16	2	no	—
246	C₂×C₁₃₁	#2620	1	1	yes	characteristic
247	C₂×C₁₃₁	#3057	1	1	yes	characteristic
248	C₂×C₁₃₁	#3058	1	1	yes	characteristic
249	C₂×C₁₃₁	#3224	1	2	yes	—
250	C₂×C₁₃₁	#3241	1	2	yes	—
251	#29847	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
252	C₁₃₁	#29847	1	1	yes	characteristic, direct product factor, Sylow
253	C₂×#486	C₂×C₁₃₁	1	1	yes	characteristic, complemented
254	C₂×#433	C₂×C₁₃₁	1	1	yes	characteristic, complemented
255	#2628	C₂×C₁₃₁	1	1	yes	characteristic, complemented
256	#2619	C₂×C₁₃₁	1	1	yes	characteristic
257	#2067	C₂×C₁₃₁	1	2	yes	complemented
258	#2065	C₂×C₁₃₁	1	2	yes	complemented
259	#2034	C₂×C₁₃₁	1	2	yes	complemented
260	#2033	C₂×C₁₃₁	1	2	yes	complemented
261	#1993	C₂×C₁₃₁	1	1	yes	characteristic, complemented
262	#1961	C₂×C₁₃₁	1	1	yes	characteristic, complemented
263	#1846	C₂×C₁₃₁	1	1	yes	characteristic, complemented
264	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
265	C₂×#127	C₂²×C₁₃₁	1	1	yes	characteristic
266	C₂×#121	C₂²×C₁₃₁	1	2	yes	—
267	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
268	#486	—	2	4	no	—
269	#433	—	2	4	no	—
270	C₂×#107	C₂²×C₁₃₁	1	2	yes	—
271	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
272	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
273	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
274	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
275	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
276	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
277	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
278	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
279	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
280	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
281	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
282	#400	—	2	1	no	—
283	#399	—	2	1	no	—
284	#395	—	2	1	no	—
285	#394	—	2	1	no	—
286	#394	—	2	1	no	—
287	#393	—	2	1	no	—
288	#392	—	2	1	no	—
289	#392	—	2	1	no	—
290	#390	C₂²×C₁₃₁	1	2	yes	—
291	#389	C₂²×C₁₃₁	1	2	yes	—
292	#382	C₂²×C₁₃₁	1	1	yes	characteristic
293	#382	C₂²×C₁₃₁	1	1	yes	characteristic
294	#380	C₂²×C₁₃₁	1	2	yes	—
295	#340	C₂²×C₁₃₁	1	2	yes	—
296	#340	C₂²×C₁₃₁	1	2	yes	—
297	C₂²×Q₈	—	2	1	no	—
298	C₂²×D₄	—	2	2	no	—
299	C₂²×D₄	—	2	1	no	—
300	C₂²×D₄	—	2	1	no	—
301	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
302	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
303	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
307	C₄⋊Q₈	—	2	2	no	—
308	C₄⋊Q₈	—	2	2	no	—
309	#127	—	2	2	no	—
310	#127	—	2	2	no	—
311	#121	—	4	2	no	—
312	#121	—	4	2	no	—
313	#117	—	2	2	no	—
314	#117	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
318	C₂×C₄⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
327	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
328	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
330	#107	—	4	2	no	—
331	#106	—	4	2	no	—
332	C₄⋊C₈	—	2	2	no	—
333	C₄⋊C₈	—	2	2	no	—
334	#102	—	2	4	no	—
335	#102	—	2	4	no	—
336	#102	—	4	2	no	—
337	#102	—	4	2	no	—
338	C₂²⋊C₈	—	2	2	no	—
339	C₂²⋊C₈	—	2	2	no	—
340	#97	—	2	2	no	—
341	C₄×C₈	D₄×C₁₃₁	1	4	yes	complemented
342	#95	—	2	2	no	—
343	#95	—	2	1	no	—
344	#95	—	2	1	no	—
345	#95	—	2	1	no	—
346	#95	—	2	1	no	—
347	#95	—	2	2	no	—
348	C₂⁴	—	2	2	no	—
349	C₂⁴	C₂×D₄×C₁₃₁	1	1	yes	characteristic
350	C₂×Q₈	—	4	2	no	—
351	C₂×Q₈	—	8	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	4	4	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	—	8	2	no	—
362	C₂×D₄	—	8	2	no	—
363	C₂×D₄	—	8	2	no	—
364	C₂×D₄	—	8	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
379	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
391	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	4	2	no	—
401	C₄⋊C₄	—	8	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	4	4	no	—
405	C₂²⋊C₄	—	8	2	no	—
406	C₂²⋊C₄	—	8	2	no	—
407	C₂²⋊C₄	—	8	2	no	—
408	C₄²	—	2	1	no	—
409	C₄²	—	2	1	no	—
410	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
411	C₄²	#41×C₁₃₁	1	2	yes	—
412	C₂³	—	2	1	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
425	Q₈	—	8	4	no	—
426	D₄	—	4	2	no	—
427	D₄	—	4	2	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	2	no	—
430	D₄	—	8	4	no	—
431	D₄	—	8	4	no	—
432	D₄	—	8	8	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	#121×C₁₃₁	1	2	yes	—
456	C₂×C₄	#121×C₁₃₁	1	2	yes	—
457	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
458	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
459	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
460	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
461	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
462	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
463	C₈	—	2	2	no	—
464	C₈	—	2	2	no	—
465	C₈	—	4	1	no	—
466	C₈	—	4	1	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	4	1	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	8	2	no	—
473	C₂²	—	8	2	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
480	C₂²	#535×C₁₃₁	1	1	yes	characteristic
481	C₂²	#536×C₁₃₁	1	1	yes	characteristic
482	C₂²	#576×C₁₃₁	1	2	yes	—
483	C₂²	#577×C₁₃₁	1	2	yes	—
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	4	1	no	—
487	C₄	—	4	1	no	—
488	C₄	—	4	1	no	—
489	C₄	—	8	2	no	—
490	C₄	—	8	2	no	—
491	C₄	—	8	2	no	—
492	C₄	#537×C₁₃₁	1	1	yes	characteristic
493	C₄	#537×C₁₃₁	1	1	yes	characteristic
494	C₄	#542×C₁₃₁	1	1	yes	characteristic
495	C₄	#542×C₁₃₁	1	1	yes	characteristic
496	C₂	—	8	1	no	—
497	C₂	—	16	2	no	—
498	C₂	#2620×C₁₃₁	1	1	yes	characteristic
499	C₂	#3057×C₁₃₁	1	1	yes	characteristic
500	C₂	#3058×C₁₃₁	1	1	yes	characteristic
501	C₂	#3224×C₁₃₁	1	2	yes	—
502	C₂	#3241×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	#2619×C₁₃₁	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₂×#117×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#486×C₁₃₁	C₂	semidirect
2. C₂×#433×C₁₃₁	C₂	semidirect
3. #2628×C₁₃₁	C₂	semidirect
5. #2067×C₁₃₁	C₂	semidirect
6. #2065×C₁₃₁	C₂	semidirect
7. #2034×C₁₃₁	C₂	semidirect
8. #2033×C₁₃₁	C₂	semidirect
9. #1993×C₁₃₁	C₂	semidirect
10. #1961×C₁₃₁	C₂	semidirect
11. #1846×C₁₃₁	C₂	semidirect
89. C₄×C₈×C₁₃₁	D₄	semidirect
251. #29847	C₁₃₁	direct (N × H)
252. C₁₃₁	#29847	direct (N × H)
253. C₂×#486	C₂×C₁₃₁	semidirect
254. C₂×#433	C₂×C₁₃₁	semidirect
255. #2628	C₂×C₁₃₁	semidirect
257. #2067	C₂×C₁₃₁	semidirect
258. #2065	C₂×C₁₃₁	semidirect
259. #2034	C₂×C₁₃₁	semidirect
260. #2033	C₂×C₁₃₁	semidirect
261. #1993	C₂×C₁₃₁	semidirect
262. #1961	C₂×C₁₃₁	semidirect
263. #1846	C₂×C₁₃₁	semidirect
341. C₄×C₈	D₄×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#486×C₁₃₁	2
C₂×#433×C₁₃₁	2
#2628×C₁₃₁	2
#2619×C₁₃₁	2
#2067×C₁₃₁	2
#2065×C₁₃₁	2
#2034×C₁₃₁	2
#2033×C₁₃₁	2
#1993×C₁₃₁	2
#1961×C₁₃₁	2
#1846×C₁₃₁	2
#29847	131

Subgroups — C131×#29847 #45715731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#29847 #45715731