Subgroups — C₁₃₁×#14446 #45700330

Order 33536.

1246 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#389×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#387×C₁₃₁	C₂	1	2	yes	maximal
3	#1445×C₁₃₁	C₂	1	2	yes	maximal
4	#1442×C₁₃₁	C₂	1	2	yes	maximal
5	#1441×C₁₃₁	C₂	1	2	yes	maximal
6	#1436×C₁₃₁	C₂	1	2	yes	maximal
7	#1436×C₁₃₁	C₂	1	2	yes	maximal
8	C₄⋊#95×C₁₃₁	C₂	1	1	yes	maximal, characteristic
9	C₄⋊#95×C₁₃₁	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₃₁	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
19	#389×C₁₃₁	C₄	1	8	yes	complemented
20	#387×C₁₃₁	—	2	8	no	—
21	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
22	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
23	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
24	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
25	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
26	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
27	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
28	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
29	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
30	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
31	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
32	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
33	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
34	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
35	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
43	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
45	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
46	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₃₁	—	4	1	no	—
49	C₂×C₄⋊C₄×C₁₃₁	—	4	1	no	—
50	C₂×C₄⋊C₄×C₁₃₁	—	4	1	no	—
51	C₂×C₄⋊C₄×C₁₃₁	—	4	1	no	—
52	C₂×C₄⋊C₄×C₁₃₁	—	4	1	no	—
53	C₂×C₄⋊C₄×C₁₃₁	—	4	1	no	—
54	C₂×C₄⋊C₄×C₁₃₁	—	4	1	no	—
55	C₂×C₄⋊C₄×C₁₃₁	—	4	1	no	—
56	C₂×C₄⋊C₄×C₁₃₁	—	4	1	no	—
57	C₂×C₄⋊C₄×C₁₃₁	—	4	1	no	—
58	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	4	yes	—
59	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	8	yes	—
60	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₃₁	D₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₃₁	Q₈	1	4	yes	—
63	C₂×C₄²×C₁₃₁	—	2	4	no	—
64	C₂×C₄²×C₁₃₁	—	4	1	no	—
65	C₂×C₄²×C₁₃₁	—	4	1	no	—
66	C₂×C₄²×C₁₃₁	—	4	2	no	—
67	C₂×C₄²×C₁₃₁	—	4	2	no	—
68	C₂×C₄²×C₁₃₁	C₂×C₄	1	4	yes	—
69	#95×C₁₃₁	—	2	4	no	—
70	#95×C₁₃₁	—	2	4	no	—
71	#95×C₁₃₁	—	2	4	no	—
72	#95×C₁₃₁	—	2	4	no	—
73	#95×C₁₃₁	—	2	4	no	—
74	#95×C₁₃₁	—	2	4	no	—
75	#95×C₁₃₁	—	2	4	no	—
76	#95×C₁₃₁	—	4	2	no	—
77	#95×C₁₃₁	—	4	2	no	—
78	#95×C₁₃₁	—	4	2	no	—
79	#95×C₁₃₁	—	4	2	no	—
80	#95×C₁₃₁	C₂×C₄	1	8	yes	—
81	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
82	C₂²×C₄×C₁₃₁	—	2	1	no	—
83	C₂²×C₄×C₁₃₁	—	2	1	no	—
84	C₂²×C₄×C₁₃₁	—	2	1	no	—
85	C₂²×C₄×C₁₃₁	—	2	1	no	—
86	C₂²×C₄×C₁₃₁	—	2	1	no	—
87	C₂²×C₄×C₁₃₁	—	2	1	no	—
88	C₂²×C₄×C₁₃₁	—	2	1	no	—
89	C₂²×C₄×C₁₃₁	—	2	1	no	—
90	C₂²×C₄×C₁₃₁	—	2	1	no	—
91	C₂²×C₄×C₁₃₁	—	2	1	no	—
92	C₂²×C₄×C₁₃₁	—	2	1	no	—
93	C₂²×C₄×C₁₃₁	—	2	1	no	—
94	C₂²×C₄×C₁₃₁	—	2	2	no	—
95	C₂²×C₄×C₁₃₁	—	2	2	no	—
96	C₂²×C₄×C₁₃₁	—	2	2	no	—
97	C₂²×C₄×C₁₃₁	—	2	2	no	—
98	C₂²×C₄×C₁₃₁	—	2	2	no	—
99	C₂²×C₄×C₁₃₁	—	2	2	no	—
100	C₂²×C₄×C₁₃₁	—	2	2	no	—
101	C₂²×C₄×C₁₃₁	—	2	2	no	—
102	C₂²×C₄×C₁₃₁	—	2	2	no	—
103	C₂²×C₄×C₁₃₁	—	2	2	no	—
104	C₂²×C₄×C₁₃₁	—	2	2	no	—
105	C₂²×C₄×C₁₃₁	—	2	2	no	—
106	C₂²×C₄×C₁₃₁	—	2	2	no	—
107	C₂²×C₄×C₁₃₁	—	2	2	no	—
108	C₂²×C₄×C₁₃₁	—	2	2	no	—
109	C₂²×C₄×C₁₃₁	—	2	2	no	—
110	C₂²×C₄×C₁₃₁	—	2	2	no	—
111	C₂²×C₄×C₁₃₁	—	2	2	no	—
112	C₂²×C₄×C₁₃₁	—	2	2	no	—
113	C₂²×C₄×C₁₃₁	—	2	2	no	—
114	C₂²×C₄×C₁₃₁	—	2	2	no	—
115	C₂²×C₄×C₁₃₁	—	2	2	no	—
116	C₂²×C₄×C₁₃₁	—	2	2	no	—
117	C₂²×C₄×C₁₃₁	—	2	2	no	—
118	C₂²×C₄×C₁₃₁	—	2	2	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	—	2	2	no	—
123	C₂²×C₄×C₁₃₁	—	2	2	no	—
124	C₂²×C₄×C₁₃₁	—	2	2	no	—
125	C₂²×C₄×C₁₃₁	—	2	2	no	—
126	C₂²×C₄×C₁₃₁	—	2	2	no	—
127	C₂²×C₄×C₁₃₁	—	2	2	no	—
128	C₂²×C₄×C₁₃₁	—	2	2	no	—
129	C₂²×C₄×C₁₃₁	—	2	2	no	—
130	C₂²×C₄×C₁₃₁	—	2	2	no	—
131	C₂²×C₄×C₁₃₁	—	2	2	no	—
132	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
133	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
134	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₃₁	C₂×Q₈	1	4	yes	—
140	C₂²×C₄×C₁₃₁	C₂×Q₈	1	2	yes	—
141	C₂²×C₄×C₁₃₁	#41	1	2	yes	—
142	C₂²×C₄×C₁₃₁	#41	1	2	yes	—
143	C₂²×C₄×C₁₃₁	#41	1	2	yes	—
144	C₂²×C₄×C₁₃₁	#41	1	2	yes	—
145	C₄⋊C₄×C₁₃₁	—	2	8	no	—
146	C₄⋊C₄×C₁₃₁	—	2	16	no	—
147	C₄⋊C₄×C₁₃₁	—	4	4	no	—
148	C₄⋊C₄×C₁₃₁	—	4	4	no	—
149	C₄⋊C₄×C₁₃₁	—	4	4	no	—
150	C₄⋊C₄×C₁₃₁	—	4	4	no	—
151	C₄⋊C₄×C₁₃₁	—	4	4	no	—
152	C₄²×C₁₃₁	—	4	4	no	—
153	C₄²×C₁₃₁	—	4	8	no	—
154	C₂³×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
155	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
156	C₂³×C₁₃₁	C₂²×Q₈	1	1	yes	characteristic
157	C₂³×C₁₃₁	C₂×#41	1	1	yes	characteristic
158	C₂³×C₁₃₁	C₂×#41	1	1	yes	characteristic
159	C₂³×C₁₃₁	C₂×#41	1	1	yes	characteristic
160	C₂³×C₁₃₁	C₂×#41	1	1	yes	characteristic
161	C₂³×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
162	C₂³×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
163	C₂³×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
164	C₂³×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
165	C₂³×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
166	C₂³×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
167	C₂³×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
168	C₂³×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
169	C₂×C₄×C₁₃₁	—	2	2	no	—
170	C₂×C₄×C₁₃₁	—	2	2	no	—
171	C₂×C₄×C₁₃₁	—	2	2	no	—
172	C₂×C₄×C₁₃₁	—	2	2	no	—
173	C₂×C₄×C₁₃₁	—	2	2	no	—
174	C₂×C₄×C₁₃₁	—	2	2	no	—
175	C₂×C₄×C₁₃₁	—	2	2	no	—
176	C₂×C₄×C₁₃₁	—	2	2	no	—
177	C₂×C₄×C₁₃₁	—	2	2	no	—
178	C₂×C₄×C₁₃₁	—	2	2	no	—
179	C₂×C₄×C₁₃₁	—	2	2	no	—
180	C₂×C₄×C₁₃₁	—	2	2	no	—
181	C₂×C₄×C₁₃₁	—	2	2	no	—
182	C₂×C₄×C₁₃₁	—	2	2	no	—
183	C₂×C₄×C₁₃₁	—	2	2	no	—
184	C₂×C₄×C₁₃₁	—	2	2	no	—
185	C₂×C₄×C₁₃₁	—	2	2	no	—
186	C₂×C₄×C₁₃₁	—	2	2	no	—
187	C₂×C₄×C₁₃₁	—	2	4	no	—
188	C₂×C₄×C₁₃₁	—	2	4	no	—
189	C₂×C₄×C₁₃₁	—	2	4	no	—
190	C₂×C₄×C₁₃₁	—	2	4	no	—
191	C₂×C₄×C₁₃₁	—	2	4	no	—
192	C₂×C₄×C₁₃₁	—	2	4	no	—
193	C₂×C₄×C₁₃₁	—	2	4	no	—
194	C₂×C₄×C₁₃₁	—	2	4	no	—
195	C₂×C₄×C₁₃₁	—	2	4	no	—
196	C₂×C₄×C₁₃₁	—	2	4	no	—
197	C₂×C₄×C₁₃₁	—	2	4	no	—
198	C₂×C₄×C₁₃₁	—	2	4	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	—	4	2	no	—
204	C₂×C₄×C₁₃₁	—	4	2	no	—
205	C₂×C₄×C₁₃₁	—	4	2	no	—
206	C₂×C₄×C₁₃₁	—	4	2	no	—
207	C₂×C₄×C₁₃₁	—	4	2	no	—
208	C₂×C₄×C₁₃₁	—	4	2	no	—
209	C₂×C₄×C₁₃₁	—	4	2	no	—
210	C₂×C₄×C₁₃₁	—	4	2	no	—
211	C₂×C₄×C₁₃₁	—	4	2	no	—
212	C₂×C₄×C₁₃₁	—	4	2	no	—
213	C₂×C₄×C₁₃₁	—	4	2	no	—
214	C₂×C₄×C₁₃₁	—	4	2	no	—
215	C₂×C₄×C₁₃₁	—	4	2	no	—
216	C₂×C₄×C₁₃₁	—	4	2	no	—
217	C₂×C₄×C₁₃₁	—	4	2	no	—
218	C₂×C₄×C₁₃₁	—	4	2	no	—
219	C₂×C₄×C₁₃₁	—	4	2	no	—
220	C₂×C₄×C₁₃₁	—	4	2	no	—
221	C₂×C₄×C₁₃₁	—	4	2	no	—
222	C₂×C₄×C₁₃₁	—	4	2	no	—
223	C₂×C₄×C₁₃₁	—	4	2	no	—
224	C₂×C₄×C₁₃₁	—	4	2	no	—
225	C₂×C₄×C₁₃₁	—	4	2	no	—
226	C₂×C₄×C₁₃₁	—	4	2	no	—
227	C₂×C₄×C₁₃₁	—	4	2	no	—
228	C₂×C₄×C₁₃₁	—	4	2	no	—
229	C₂×C₄×C₁₃₁	#117	1	4	yes	—
230	C₂×C₄×C₁₃₁	C₄×D₄	1	4	yes	—
231	C₂×C₄×C₁₃₁	C₄×Q₈	1	4	yes	—
232	C₂²×C₁₃₁	C₂×#117	1	1	yes	characteristic
233	C₂²×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
234	C₂²×C₁₃₁	C₂×C₄×Q₈	1	1	yes	characteristic
235	C₂²×C₁₃₁	#518	1	1	yes	characteristic
236	C₂²×C₁₃₁	#519	1	1	yes	characteristic
237	C₂²×C₁₃₁	#520	1	1	yes	characteristic
238	C₂²×C₁₃₁	#520	1	1	yes	characteristic
239	C₂²×C₁₃₁	#534	1	1	yes	characteristic
240	C₂²×C₁₃₁	#537	1	1	yes	characteristic
241	C₂²×C₁₃₁	#538	1	1	yes	characteristic
242	C₂²×C₁₃₁	#538	1	1	yes	characteristic
243	C₂²×C₁₃₁	#539	1	1	yes	characteristic
244	C₂²×C₁₃₁	#539	1	1	yes	characteristic
245	C₂²×C₁₃₁	#539	1	1	yes	characteristic
246	C₂²×C₁₃₁	#539	1	1	yes	characteristic
247	C₂²×C₁₃₁	#539	1	1	yes	characteristic
248	C₂²×C₁₃₁	#539	1	1	yes	characteristic
249	C₂²×C₁₃₁	#543	1	1	yes	characteristic
250	C₂²×C₁₃₁	#544	1	1	yes	characteristic
251	C₂²×C₁₃₁	#547	1	1	yes	characteristic
252	C₂²×C₁₃₁	#547	1	1	yes	characteristic
253	C₂²×C₁₃₁	D₄×Q₈	1	1	yes	characteristic
254	C₂²×C₁₃₁	#550	1	1	yes	characteristic
255	C₂²×C₁₃₁	#554	1	1	yes	characteristic
256	C₂²×C₁₃₁	#555	1	1	yes	characteristic
257	C₂²×C₁₃₁	#556	1	1	yes	characteristic
258	C₂²×C₁₃₁	#556	1	1	yes	characteristic
259	C₂²×C₁₃₁	#556	1	1	yes	characteristic
260	C₂²×C₁₃₁	#557	1	1	yes	characteristic
261	C₂²×C₁₃₁	#557	1	1	yes	characteristic
262	C₂²×C₁₃₁	#559	1	1	yes	characteristic
263	C₂²×C₁₃₁	#562	1	1	yes	characteristic
264	C₂²×C₁₃₁	#563	1	1	yes	characteristic
265	C₂²×C₁₃₁	#563	1	1	yes	characteristic
266	C₂²×C₁₃₁	#564	1	1	yes	characteristic
267	C₄×C₁₃₁	—	2	4	no	—
268	C₄×C₁₃₁	—	2	4	no	—
269	C₄×C₁₃₁	—	2	4	no	—
270	C₄×C₁₃₁	—	4	4	no	—
271	C₄×C₁₃₁	—	4	4	no	—
272	C₄×C₁₃₁	—	4	4	no	—
273	C₄×C₁₃₁	—	4	4	no	—
274	C₄×C₁₃₁	—	8	2	no	—
275	C₄×C₁₃₁	—	8	2	no	—
276	C₂×C₁₃₁	#2313	1	1	yes	characteristic
277	C₂×C₁₃₁	#2325	1	1	yes	characteristic
278	C₂×C₁₃₁	#2329	1	1	yes	characteristic
279	C₂×C₁₃₁	#2354	1	1	yes	characteristic
280	C₂×C₁₃₁	#2355	1	1	yes	characteristic
281	C₂×C₁₃₁	#2365	1	1	yes	characteristic
282	C₂×C₁₃₁	#2382	1	1	yes	characteristic
283	C₂×C₁₃₁	#2724	1	1	yes	characteristic
284	C₂×C₁₃₁	#2726	1	1	yes	characteristic
285	C₂×C₁₃₁	#2727	1	1	yes	characteristic
286	C₂×C₁₃₁	#2732	1	1	yes	characteristic
287	C₂×C₁₃₁	#2805	1	1	yes	characteristic
288	C₂×C₁₃₁	#2808	1	1	yes	characteristic
289	C₂×C₁₃₁	#2809	1	1	yes	characteristic
290	C₂×C₁₃₁	#2810	1	1	yes	characteristic
291	#14446	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
292	C₁₃₁	#14446	1	1	yes	characteristic, direct product factor, Sylow
293	C₂×#389	C₂×C₁₃₁	1	1	yes	characteristic
294	C₂×#387	C₂×C₁₃₁	1	2	yes	—
295	#1445	C₂×C₁₃₁	1	2	yes	—
296	#1442	C₂×C₁₃₁	1	2	yes	—
297	#1441	C₂×C₁₃₁	1	2	yes	—
298	#1436	C₂×C₁₃₁	1	2	yes	—
299	#1436	C₂×C₁₃₁	1	2	yes	—
300	C₄⋊#95	C₂×C₁₃₁	1	1	yes	characteristic
301	C₄⋊#95	C₂×C₁₃₁	1	1	yes	characteristic
302	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
303	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
304	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
305	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
306	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
307	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
308	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
309	C₂²×C₄²	C₂²×C₁₃₁	1	2	yes	—
310	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
311	#389	C₄×C₁₃₁	1	8	yes	complemented
312	#387	—	2	8	no	—
313	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
314	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
315	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
316	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
317	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
318	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
319	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
320	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
321	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
322	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
323	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
324	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
325	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
326	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
327	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
328	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
329	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
330	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
331	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
332	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
333	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
334	C₂×C₄⋊C₄	—	2	4	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	4	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	2	no	—
340	C₂×C₄⋊C₄	—	4	1	no	—
341	C₂×C₄⋊C₄	—	4	1	no	—
342	C₂×C₄⋊C₄	—	4	1	no	—
343	C₂×C₄⋊C₄	—	4	1	no	—
344	C₂×C₄⋊C₄	—	4	1	no	—
345	C₂×C₄⋊C₄	—	4	1	no	—
346	C₂×C₄⋊C₄	—	4	1	no	—
347	C₂×C₄⋊C₄	—	4	1	no	—
348	C₂×C₄⋊C₄	—	4	1	no	—
349	C₂×C₄⋊C₄	—	4	1	no	—
350	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	4	yes	—
351	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	8	yes	—
352	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	4	yes	—
353	C₂×C₄⋊C₄	D₄×C₁₃₁	1	4	yes	—
354	C₂×C₄⋊C₄	Q₈×C₁₃₁	1	4	yes	—
355	C₂×C₄²	—	2	4	no	—
356	C₂×C₄²	—	4	1	no	—
357	C₂×C₄²	—	4	1	no	—
358	C₂×C₄²	—	4	2	no	—
359	C₂×C₄²	—	4	2	no	—
360	C₂×C₄²	C₂×C₄×C₁₃₁	1	4	yes	—
361	#95	—	2	4	no	—
362	#95	—	2	4	no	—
363	#95	—	2	4	no	—
364	#95	—	2	4	no	—
365	#95	—	2	4	no	—
366	#95	—	2	4	no	—
367	#95	—	2	4	no	—
368	#95	—	4	2	no	—
369	#95	—	4	2	no	—
370	#95	—	4	2	no	—
371	#95	—	4	2	no	—
372	#95	C₂×C₄×C₁₃₁	1	8	yes	—
373	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
425	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
426	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
427	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
428	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
429	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
430	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
431	C₂²×C₄	C₂×Q₈×C₁₃₁	1	4	yes	—
432	C₂²×C₄	C₂×Q₈×C₁₃₁	1	2	yes	—
433	C₂²×C₄	#41×C₁₃₁	1	2	yes	—
434	C₂²×C₄	#41×C₁₃₁	1	2	yes	—
435	C₂²×C₄	#41×C₁₃₁	1	2	yes	—
436	C₂²×C₄	#41×C₁₃₁	1	2	yes	—
437	C₄⋊C₄	—	2	8	no	—
438	C₄⋊C₄	—	2	16	no	—
439	C₄⋊C₄	—	4	4	no	—
440	C₄⋊C₄	—	4	4	no	—
441	C₄⋊C₄	—	4	4	no	—
442	C₄⋊C₄	—	4	4	no	—
443	C₄⋊C₄	—	4	4	no	—
444	C₄²	—	4	4	no	—
445	C₄²	—	4	8	no	—
446	C₂³	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
447	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
448	C₂³	C₂²×Q₈×C₁₃₁	1	1	yes	characteristic
449	C₂³	C₂×#41×C₁₃₁	1	1	yes	characteristic
450	C₂³	C₂×#41×C₁₃₁	1	1	yes	characteristic
451	C₂³	C₂×#41×C₁₃₁	1	1	yes	characteristic
452	C₂³	C₂×#41×C₁₃₁	1	1	yes	characteristic
453	C₂³	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
454	C₂³	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
455	C₂³	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
456	C₂³	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
457	C₂³	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
458	C₂³	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
459	C₂³	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
460	C₂³	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	#117×C₁₃₁	1	4	yes	—
522	C₂×C₄	C₄×D₄×C₁₃₁	1	4	yes	—
523	C₂×C₄	C₄×Q₈×C₁₃₁	1	4	yes	—
524	C₂²	C₂×#117×C₁₃₁	1	1	yes	characteristic
525	C₂²	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
526	C₂²	C₂×C₄×Q₈×C₁₃₁	1	1	yes	characteristic
527	C₂²	#518×C₁₃₁	1	1	yes	characteristic
528	C₂²	#519×C₁₃₁	1	1	yes	characteristic
529	C₂²	#520×C₁₃₁	1	1	yes	characteristic
530	C₂²	#520×C₁₃₁	1	1	yes	characteristic
531	C₂²	#534×C₁₃₁	1	1	yes	characteristic
532	C₂²	#537×C₁₃₁	1	1	yes	characteristic
533	C₂²	#538×C₁₃₁	1	1	yes	characteristic
534	C₂²	#538×C₁₃₁	1	1	yes	characteristic
535	C₂²	#539×C₁₃₁	1	1	yes	characteristic
536	C₂²	#539×C₁₃₁	1	1	yes	characteristic
537	C₂²	#539×C₁₃₁	1	1	yes	characteristic
538	C₂²	#539×C₁₃₁	1	1	yes	characteristic
539	C₂²	#539×C₁₃₁	1	1	yes	characteristic
540	C₂²	#539×C₁₃₁	1	1	yes	characteristic
541	C₂²	#543×C₁₃₁	1	1	yes	characteristic
542	C₂²	#544×C₁₃₁	1	1	yes	characteristic
543	C₂²	#547×C₁₃₁	1	1	yes	characteristic
544	C₂²	#547×C₁₃₁	1	1	yes	characteristic
545	C₂²	D₄×Q₈×C₁₃₁	1	1	yes	characteristic
546	C₂²	#550×C₁₃₁	1	1	yes	characteristic
547	C₂²	#554×C₁₃₁	1	1	yes	characteristic
548	C₂²	#555×C₁₃₁	1	1	yes	characteristic
549	C₂²	#556×C₁₃₁	1	1	yes	characteristic
550	C₂²	#556×C₁₃₁	1	1	yes	characteristic
551	C₂²	#556×C₁₃₁	1	1	yes	characteristic
552	C₂²	#557×C₁₃₁	1	1	yes	characteristic
553	C₂²	#557×C₁₃₁	1	1	yes	characteristic
554	C₂²	#559×C₁₃₁	1	1	yes	characteristic
555	C₂²	#562×C₁₃₁	1	1	yes	characteristic
556	C₂²	#563×C₁₃₁	1	1	yes	characteristic
557	C₂²	#563×C₁₃₁	1	1	yes	characteristic
558	C₂²	#564×C₁₃₁	1	1	yes	characteristic
559	C₄	—	2	4	no	—
560	C₄	—	2	4	no	—
561	C₄	—	2	4	no	—
562	C₄	—	4	4	no	—
563	C₄	—	4	4	no	—
564	C₄	—	4	4	no	—
565	C₄	—	4	4	no	—
566	C₄	—	8	2	no	—
567	C₄	—	8	2	no	—
568	C₂	#2313×C₁₃₁	1	1	yes	characteristic
569	C₂	#2325×C₁₃₁	1	1	yes	characteristic
570	C₂	#2329×C₁₃₁	1	1	yes	characteristic
571	C₂	#2354×C₁₃₁	1	1	yes	characteristic
572	C₂	#2355×C₁₃₁	1	1	yes	characteristic
573	C₂	#2365×C₁₃₁	1	1	yes	characteristic
574	C₂	#2382×C₁₃₁	1	1	yes	characteristic
575	C₂	#2724×C₁₃₁	1	1	yes	characteristic
576	C₂	#2726×C₁₃₁	1	1	yes	characteristic
577	C₂	#2727×C₁₃₁	1	1	yes	characteristic
578	C₂	#2732×C₁₃₁	1	1	yes	characteristic
579	C₂	#2805×C₁₃₁	1	1	yes	characteristic
580	C₂	#2808×C₁₃₁	1	1	yes	characteristic
581	C₂	#2809×C₁₃₁	1	1	yes	characteristic
582	C₂	#2810×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
19. #389×C₁₃₁	C₄	semidirect
291. #14446	C₁₃₁	direct (N × H)
292. C₁₃₁	#14446	direct (N × H)
311. #389	C₄×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#389×C₁₃₁	2
C₂×#387×C₁₃₁	2
#1445×C₁₃₁	2
#1442×C₁₃₁	2
#1441×C₁₃₁	2
#1436×C₁₃₁	2
C₄⋊#95×C₁₃₁	2
#14446	131

Subgroups — C131×#14446 #45700330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#14446 #45700330