Subgroups — C₁₃₁×#29904 #45715788

Order 33536.

746 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3010×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2889×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2082×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2080×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2048×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2046×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#1914×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1910×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1868×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1858×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1796×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×AGL(1,ℤ/8)×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
15	#568×C₁₃₁	C₂²	1	1	yes	characteristic
16	#568×C₁₃₁	C₂²	1	1	yes	characteristic
17	#535×C₁₃₁	C₂²	1	1	yes	characteristic
18	#449×C₁₃₁	—	2	2	no	—
19	#448×C₁₃₁	—	2	2	no	—
20	#430×C₁₃₁	C₂²	1	2	yes	—
21	#424×C₁₃₁	C₂²	1	2	yes	—
22	#421×C₁₃₁	C₂²	1	2	yes	—
23	#419×C₁₃₁	C₂²	1	1	yes	characteristic
24	#419×C₁₃₁	C₂²	1	2	yes	—
25	#418×C₁₃₁	C₂²	1	2	yes	—
26	#416×C₁₃₁	C₂²	1	1	yes	characteristic
27	#413×C₁₃₁	—	2	2	no	—
28	#413×C₁₃₁	C₂²	1	2	yes	—
29	#413×C₁₃₁	C₂²	1	1	yes	characteristic
30	C₂×#101×C₁₃₁	—	2	2	no	—
31	C₂×#101×C₁₃₁	C₂²	1	2	yes	—
32	C₂×#100×C₁₃₁	C₂²	1	2	yes	—
33	#410×C₁₃₁	C₂²	1	1	yes	characteristic
34	#408×C₁₃₁	C₂²	1	1	yes	characteristic
35	#344×C₁₃₁	C₂²	1	2	yes	—
36	#344×C₁₃₁	C₂²	1	2	yes	—
37	#341×C₁₃₁	C₂²	1	2	yes	—
38	H(3,ℤ/4)×C₁₃₁	C₂²	1	2	yes	—
39	2₋¹⁺⁴×C₁₃₁	—	4	2	no	—
40	2₋¹⁺⁴×C₁₃₁	—	4	2	no	—
41	C₂×#41×C₁₃₁	—	2	1	no	—
42	C₂×#41×C₁₃₁	—	2	2	no	—
43	C₂×#41×C₁₃₁	D₄	1	2	yes	—
44	C₂×#41×C₁₃₁	C₂³	1	1	yes	characteristic
45	C₂×#41×C₁₃₁	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃₁	—	2	1	no	—
47	C₂²×Q₈×C₁₃₁	D₄	1	2	yes	—
48	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
50	AGL(1,ℤ/8)×C₁₃₁	—	4	2	no	—
51	C₂×SD₁₆×C₁₃₁	—	2	1	no	—
52	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
53	C₂×SD₁₆×C₁₃₁	—	4	2	no	—
54	C₂×D₈×C₁₃₁	—	2	1	no	—
55	#131×C₁₃₁	—	4	2	no	—
56	#131×C₁₃₁	—	4	2	no	—
57	C₂×M₁₆×C₁₃₁	—	2	2	no	—
58	C₂×M₁₆×C₁₃₁	—	2	2	no	—
59	C₂×M₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
61	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
62	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
63	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
64	#127×C₁₃₁	—	2	1	no	—
65	#124×C₁₃₁	—	2	1	no	—
66	#121×C₁₃₁	—	2	2	no	—
67	#120×C₁₃₁	—	2	2	no	—
68	#117×C₁₃₁	C₂³	1	2	yes	—
69	#117×C₁₃₁	C₂³	1	1	yes	characteristic
70	#108×C₁₃₁	—	4	2	no	—
71	C₄⋊C₈×C₁₃₁	—	4	2	no	—
72	#104×C₁₃₁	—	4	2	no	—
73	#103×C₁₃₁	—	2	1	no	—
74	#103×C₁₃₁	—	2	2	no	—
75	#103×C₁₃₁	—	4	2	no	—
76	#102×C₁₃₁	—	2	1	no	—
77	#102×C₁₃₁	—	4	2	no	—
78	#101×C₁₃₁	—	2	2	no	—
79	#101×C₁₃₁	—	2	4	no	—
80	#101×C₁₃₁	—	2	1	no	—
81	#100×C₁₃₁	—	2	2	no	—
82	#100×C₁₃₁	—	2	1	no	—
83	#100×C₁₃₁	—	4	2	no	—
84	#99×C₁₃₁	—	2	2	no	—
85	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
86	C₂⁴×C₁₃₁	—	2	1	no	—
87	#41×C₁₃₁	—	2	2	no	—
88	#41×C₁₃₁	—	2	2	no	—
89	#41×C₁₃₁	—	2	2	no	—
90	#41×C₁₃₁	—	2	2	no	—
91	#41×C₁₃₁	—	4	2	no	—
92	#41×C₁₃₁	—	4	2	no	—
93	#41×C₁₃₁	—	4	8	no	—
94	#41×C₁₃₁	—	4	4	no	—
95	C₂×Q₈×C₁₃₁	—	2	2	no	—
96	C₂×Q₈×C₁₃₁	—	2	1	no	—
97	C₂×Q₈×C₁₃₁	—	2	2	no	—
98	C₂×Q₈×C₁₃₁	—	2	2	no	—
99	C₂×Q₈×C₁₃₁	—	4	2	no	—
100	C₂×Q₈×C₁₃₁	—	4	2	no	—
101	C₂×Q₈×C₁₃₁	—	4	4	no	—
102	C₂×Q₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
103	C₂×Q₈×C₁₃₁	C₂×D₄	1	2	yes	—
104	C₂×Q₈×C₁₃₁	#41	1	1	yes	characteristic
105	C₂×D₄×C₁₃₁	—	2	2	no	—
106	C₂×D₄×C₁₃₁	—	2	1	no	—
107	C₂×D₄×C₁₃₁	—	2	1	no	—
108	C₂×D₄×C₁₃₁	—	2	1	no	—
109	C₂×D₄×C₁₃₁	—	2	2	no	—
110	C₂×D₄×C₁₃₁	—	2	2	no	—
111	C₂×D₄×C₁₃₁	—	4	2	no	—
112	C₂×D₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
113	C₂×D₄×C₁₃₁	#41	1	2	yes	—
114	C₂×D₄×C₁₃₁	#41	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₁	—	2	2	no	—
116	C₂²×C₄×C₁₃₁	—	2	1	no	—
117	C₂²×C₄×C₁₃₁	—	2	2	no	—
118	C₂²×C₄×C₁₃₁	—	2	1	no	—
119	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
121	SD₁₆×C₁₃₁	—	4	4	no	—
122	SD₁₆×C₁₃₁	—	4	2	no	—
123	D₈×C₁₃₁	—	4	2	no	—
124	M₁₆×C₁₃₁	—	2	2	no	—
125	M₁₆×C₁₃₁	—	2	2	no	—
126	M₁₆×C₁₃₁	—	2	2	no	—
127	M₁₆×C₁₃₁	—	2	2	no	—
128	M₁₆×C₁₃₁	—	2	2	no	—
129	M₁₆×C₁₃₁	—	2	2	no	—
130	M₁₆×C₁₃₁	—	2	2	no	—
131	M₁₆×C₁₃₁	—	4	2	no	—
132	M₁₆×C₁₃₁	—	4	2	no	—
133	C₂×C₈×C₁₃₁	—	2	1	no	—
134	C₂×C₈×C₁₃₁	—	2	1	no	—
135	C₂×C₈×C₁₃₁	—	2	2	no	—
136	C₂×C₈×C₁₃₁	—	2	2	no	—
137	C₂×C₈×C₁₃₁	—	2	2	no	—
138	C₂×C₈×C₁₃₁	—	2	2	no	—
139	C₂×C₈×C₁₃₁	—	4	2	no	—
140	C₂×C₈×C₁₃₁	—	4	2	no	—
141	C₄⋊C₄×C₁₃₁	—	2	1	no	—
142	C₄⋊C₄×C₁₃₁	—	2	2	no	—
143	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
144	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
145	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
146	C₄²×C₁₃₁	—	2	1	no	—
147	C₄²×C₁₃₁	—	2	2	no	—
148	C₂³×C₁₃₁	—	2	1	no	—
149	C₂³×C₁₃₁	—	4	1	no	—
150	C₂³×C₁₃₁	—	4	2	no	—
151	C₂³×C₁₃₁	—	16	1	no	—
152	C₂³×C₁₃₁	#123	1	2	yes	—
153	C₂³×C₁₃₁	C₂×#41	1	1	yes	characteristic
154	Q₈×C₁₃₁	—	2	2	no	—
155	Q₈×C₁₃₁	—	2	2	no	—
156	Q₈×C₁₃₁	—	2	1	no	—
157	Q₈×C₁₃₁	—	2	2	no	—
158	Q₈×C₁₃₁	—	2	1	no	—
159	Q₈×C₁₃₁	—	4	4	no	—
160	Q₈×C₁₃₁	—	4	2	no	—
161	D₄×C₁₃₁	—	2	4	no	—
162	D₄×C₁₃₁	—	2	1	no	—
163	D₄×C₁₃₁	—	2	1	no	—
164	D₄×C₁₃₁	—	2	2	no	—
165	D₄×C₁₃₁	—	4	4	no	—
166	D₄×C₁₃₁	—	4	2	no	—
167	D₄×C₁₃₁	—	4	1	no	—
168	D₄×C₁₃₁	—	4	1	no	—
169	D₄×C₁₃₁	—	4	2	no	—
170	D₄×C₁₃₁	—	16	2	no	—
171	C₂×C₄×C₁₃₁	—	2	2	no	—
172	C₂×C₄×C₁₃₁	—	2	2	no	—
173	C₂×C₄×C₁₃₁	—	2	1	no	—
174	C₂×C₄×C₁₃₁	—	2	2	no	—
175	C₂×C₄×C₁₃₁	—	4	4	no	—
176	C₂×C₄×C₁₃₁	—	4	4	no	—
177	C₂×C₄×C₁₃₁	—	4	2	no	—
178	C₂×C₄×C₁₃₁	—	4	2	no	—
179	C₂×C₄×C₁₃₁	—	4	1	no	—
180	C₂×C₄×C₁₃₁	—	4	2	no	—
181	C₂×C₄×C₁₃₁	#123	1	2	yes	—
182	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
185	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
186	C₈×C₁₃₁	—	4	1	no	—
187	C₈×C₁₃₁	—	4	2	no	—
188	C₈×C₁₃₁	—	4	2	no	—
189	C₈×C₁₃₁	—	4	1	no	—
190	C₈×C₁₃₁	—	4	2	no	—
191	C₂²×C₁₃₁	—	2	2	no	—
192	C₂²×C₁₃₁	—	4	1	no	—
193	C₂²×C₁₃₁	—	4	2	no	—
194	C₂²×C₁₃₁	—	4	1	no	—
195	C₂²×C₁₃₁	—	8	1	no	—
196	C₂²×C₁₃₁	—	8	2	no	—
197	C₂²×C₁₃₁	—	8	1	no	—
198	C₂²×C₁₃₁	—	16	2	no	—
199	C₂²×C₁₃₁	C₂×#123	1	1	yes	characteristic
200	C₂²×C₁₃₁	#538	1	2	yes	—
201	C₄×C₁₃₁	—	2	2	no	—
202	C₄×C₁₃₁	—	4	2	no	—
203	C₄×C₁₃₁	—	4	1	no	—
204	C₄×C₁₃₁	—	8	2	no	—
205	C₄×C₁₃₁	—	8	1	no	—
206	C₄×C₁₃₁	#534	1	1	yes	characteristic
207	C₄×C₁₃₁	#534	1	1	yes	characteristic
208	C₄×C₁₃₁	#538	1	2	yes	—
209	C₂×C₁₃₁	—	2	1	no	—
210	C₂×C₁₃₁	—	2	2	no	—
211	C₂×C₁₃₁	—	4	2	no	—
212	C₂×C₁₃₁	—	8	1	no	—
213	C₂×C₁₃₁	—	16	1	no	—
214	C₂×C₁₃₁	#2622	1	1	yes	characteristic
215	#29904	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₁₃₁	#29904	1	1	yes	characteristic, direct product factor, Sylow
217	#3010	C₂×C₁₃₁	1	1	yes	characteristic
218	#2889	C₂×C₁₃₁	1	1	yes	characteristic, complemented
219	#2082	C₂×C₁₃₁	1	2	yes	complemented
220	#2080	C₂×C₁₃₁	1	2	yes	complemented
221	#2048	C₂×C₁₃₁	1	2	yes	complemented
222	#2046	C₂×C₁₃₁	1	2	yes	complemented
223	#1914	C₂×C₁₃₁	1	1	yes	characteristic, complemented
224	#1910	C₂×C₁₃₁	1	1	yes	characteristic, complemented
225	#1868	C₂×C₁₃₁	1	1	yes	characteristic, complemented
226	#1858	C₂×C₁₃₁	1	1	yes	characteristic, complemented
227	#1796	C₂×C₁₃₁	1	1	yes	characteristic, complemented
228	C₂×2₋¹⁺⁴	C₂²×C₁₃₁	1	1	yes	characteristic
229	C₂×AGL(1,ℤ/8)	C₂²×C₁₃₁	1	1	yes	characteristic
230	C₂²×SD₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
231	#568	C₂²×C₁₃₁	1	1	yes	characteristic
232	#568	C₂²×C₁₃₁	1	1	yes	characteristic
233	#535	C₂²×C₁₃₁	1	1	yes	characteristic
234	#449	—	2	2	no	—
235	#448	—	2	2	no	—
236	#430	C₂²×C₁₃₁	1	2	yes	—
237	#424	C₂²×C₁₃₁	1	2	yes	—
238	#421	C₂²×C₁₃₁	1	2	yes	—
239	#419	C₂²×C₁₃₁	1	1	yes	characteristic
240	#419	C₂²×C₁₃₁	1	2	yes	—
241	#418	C₂²×C₁₃₁	1	2	yes	—
242	#416	C₂²×C₁₃₁	1	1	yes	characteristic
243	#413	—	2	2	no	—
244	#413	C₂²×C₁₃₁	1	2	yes	—
245	#413	C₂²×C₁₃₁	1	1	yes	characteristic
246	C₂×#101	—	2	2	no	—
247	C₂×#101	C₂²×C₁₃₁	1	2	yes	—
248	C₂×#100	C₂²×C₁₃₁	1	2	yes	—
249	#410	C₂²×C₁₃₁	1	1	yes	characteristic
250	#408	C₂²×C₁₃₁	1	1	yes	characteristic
251	#344	C₂²×C₁₃₁	1	2	yes	—
252	#344	C₂²×C₁₃₁	1	2	yes	—
253	#341	C₂²×C₁₃₁	1	2	yes	—
254	H(3,ℤ/4)	C₂²×C₁₃₁	1	2	yes	—
255	2₋¹⁺⁴	—	4	2	no	—
256	2₋¹⁺⁴	—	4	2	no	—
257	C₂×#41	—	2	1	no	—
258	C₂×#41	—	2	2	no	—
259	C₂×#41	D₄×C₁₃₁	1	2	yes	—
260	C₂×#41	C₂³×C₁₃₁	1	1	yes	characteristic
261	C₂×#41	C₂³×C₁₃₁	1	1	yes	characteristic
262	C₂²×Q₈	—	2	1	no	—
263	C₂²×Q₈	D₄×C₁₃₁	1	2	yes	—
264	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
265	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
266	AGL(1,ℤ/8)	—	4	2	no	—
267	C₂×SD₁₆	—	2	2	no	—
268	C₂×SD₁₆	—	2	1	no	—
269	C₂×SD₁₆	—	4	2	no	—
270	C₂×D₈	—	2	1	no	—
271	#131	—	4	2	no	—
272	#131	—	4	2	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	—	2	2	no	—
275	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
276	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
277	C₂×M₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
278	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
279	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
280	#127	—	2	1	no	—
281	#124	—	2	1	no	—
282	#121	—	2	2	no	—
283	#120	—	2	2	no	—
284	#117	C₂³×C₁₃₁	1	1	yes	characteristic
285	#117	C₂³×C₁₃₁	1	2	yes	—
286	#108	—	4	2	no	—
287	C₄⋊C₈	—	4	2	no	—
288	#104	—	4	2	no	—
289	#103	—	2	1	no	—
290	#103	—	2	2	no	—
291	#103	—	4	2	no	—
292	#102	—	2	1	no	—
293	#102	—	4	2	no	—
294	#101	—	2	2	no	—
295	#101	—	2	4	no	—
296	#101	—	2	1	no	—
297	#100	—	2	2	no	—
298	#100	—	2	1	no	—
299	#100	—	4	2	no	—
300	#99	—	2	2	no	—
301	C₂²⋊C₈	—	2	2	no	—
302	C₂⁴	—	2	1	no	—
303	#41	—	2	2	no	—
304	#41	—	2	2	no	—
305	#41	—	2	2	no	—
306	#41	—	2	2	no	—
307	#41	—	4	2	no	—
308	#41	—	4	2	no	—
309	#41	—	4	8	no	—
310	#41	—	4	4	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	4	2	no	—
316	C₂×Q₈	—	4	2	no	—
317	C₂×Q₈	—	4	4	no	—
318	C₂×Q₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
319	C₂×Q₈	C₂×D₄×C₁₃₁	1	2	yes	—
320	C₂×Q₈	#41×C₁₃₁	1	1	yes	characteristic
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	4	2	no	—
328	C₂×D₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
329	C₂×D₄	#41×C₁₃₁	1	2	yes	—
330	C₂×D₄	#41×C₁₃₁	1	1	yes	characteristic
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
336	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
337	SD₁₆	—	4	4	no	—
338	SD₁₆	—	4	2	no	—
339	D₈	—	4	2	no	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	2	2	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	4	2	no	—
348	M₁₆	—	4	2	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	4	2	no	—
356	C₂×C₈	—	4	2	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	2	1	no	—
361	C₂²⋊C₄	—	4	2	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	2	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	16	1	no	—
368	C₂³	#123×C₁₃₁	1	2	yes	—
369	C₂³	C₂×#41×C₁₃₁	1	1	yes	characteristic
370	Q₈	—	2	2	no	—
371	Q₈	—	2	2	no	—
372	Q₈	—	2	1	no	—
373	Q₈	—	2	2	no	—
374	Q₈	—	2	1	no	—
375	Q₈	—	4	4	no	—
376	Q₈	—	4	2	no	—
377	D₄	—	2	4	no	—
378	D₄	—	2	1	no	—
379	D₄	—	2	1	no	—
380	D₄	—	2	2	no	—
381	D₄	—	4	4	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	1	no	—
384	D₄	—	4	1	no	—
385	D₄	—	4	2	no	—
386	D₄	—	16	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	#123×C₁₃₁	1	2	yes	—
398	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
399	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
400	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
401	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
402	C₈	—	4	1	no	—
403	C₈	—	4	2	no	—
404	C₈	—	4	2	no	—
405	C₈	—	4	1	no	—
406	C₈	—	4	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	16	2	no	—
415	C₂²	C₂×#123×C₁₃₁	1	1	yes	characteristic
416	C₂²	#538×C₁₃₁	1	2	yes	—
417	C₄	—	2	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	1	no	—
420	C₄	—	8	1	no	—
421	C₄	—	8	2	no	—
422	C₄	#534×C₁₃₁	1	1	yes	characteristic
423	C₄	#534×C₁₃₁	1	1	yes	characteristic
424	C₄	#538×C₁₃₁	1	2	yes	—
425	C₂	—	2	1	no	—
426	C₂	—	2	2	no	—
427	C₂	—	4	2	no	—
428	C₂	—	8	1	no	—
429	C₂	—	16	1	no	—
430	C₂	#2622×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃₁	#2622
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	#3010×C₁₃₁	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃₁ ◁ C₂²×C₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2889×C₁₃₁	C₂	semidirect
3. #2082×C₁₃₁	C₂	semidirect
4. #2080×C₁₃₁	C₂	semidirect
5. #2048×C₁₃₁	C₂	semidirect
6. #2046×C₁₃₁	C₂	semidirect
7. #1914×C₁₃₁	C₂	semidirect
8. #1910×C₁₃₁	C₂	semidirect
9. #1868×C₁₃₁	C₂	semidirect
10. #1858×C₁₃₁	C₂	semidirect
11. #1796×C₁₃₁	C₂	semidirect
215. #29904	C₁₃₁	direct (N × H)
216. C₁₃₁	#29904	direct (N × H)
218. #2889	C₂×C₁₃₁	semidirect
219. #2082	C₂×C₁₃₁	semidirect
220. #2080	C₂×C₁₃₁	semidirect
221. #2048	C₂×C₁₃₁	semidirect
222. #2046	C₂×C₁₃₁	semidirect
223. #1914	C₂×C₁₃₁	semidirect
224. #1910	C₂×C₁₃₁	semidirect
225. #1868	C₂×C₁₃₁	semidirect
226. #1858	C₂×C₁₃₁	semidirect
227. #1796	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3010×C₁₃₁	2
#2889×C₁₃₁	2
#2082×C₁₃₁	2
#2080×C₁₃₁	2
#2048×C₁₃₁	2
#2046×C₁₃₁	2
#1914×C₁₃₁	2
#1910×C₁₃₁	2
#1868×C₁₃₁	2
#1858×C₁₃₁	2
#1796×C₁₃₁	2
#29904	131

Subgroups — C131×#29904 #45715788

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#29904 #45715788