Subgroups — C₁₃₁×#17829 #45703713

Order 33536.

610 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#41×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2925×C₁₃₁	C₂	1	2	yes	maximal
3	#1572×C₁₃₁	C₂	1	4	yes	maximal, complemented
4	#1570×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#1568×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1567×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1564×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	C₂×#335×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#41×C₁₃₁	C₂²	1	1	yes	characteristic
10	C₈×Q₈×C₁₃₁	C₄	1	1	yes	characteristic
11	C₈×Q₈×C₁₃₁	C₄	1	1	yes	characteristic
12	C₈×D₄×C₁₃₁	C₄	1	1	yes	characteristic
13	C₈×D₄×C₁₃₁	C₄	1	2	yes	—
14	C₈×D₄×C₁₃₁	C₄	1	1	yes	characteristic
15	C₈×D₄×C₁₃₁	C₄	1	2	yes	—
16	#433×C₁₃₁	—	2	4	no	—
17	#432×C₁₃₁	C₂²	1	4	yes	—
18	#431×C₁₃₁	C₂²	1	4	yes	—
19	#431×C₁₃₁	C₂²	1	1	yes	characteristic
20	#431×C₁₃₁	C₂²	1	2	yes	—
21	#423×C₁₃₁	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
23	#408×C₁₃₁	—	2	2	no	—
24	#405×C₁₃₁	—	2	2	no	—
25	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	—
27	#335×C₁₃₁	C₂²	1	1	yes	characteristic
28	#335×C₁₃₁	C₂²	1	1	yes	characteristic
29	#335×C₁₃₁	C₂²	1	2	yes	—
30	#335×C₁₃₁	C₂²	1	2	yes	—
31	#335×C₁₃₁	C₂²	1	2	yes	—
32	#334×C₁₃₁	C₂²	1	4	yes	—
33	#334×C₁₃₁	C₂²	1	4	yes	—
34	C₂×#41×C₁₃₁	D₄	1	1	yes	characteristic
35	C₂×M₁₆×C₁₃₁	—	2	2	no	—
36	C₂²×C₈×C₁₃₁	—	2	2	no	—
37	C₂²×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
39	C₂²×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
41	C₄×Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
42	C₄×Q₈×C₁₃₁	Q₈	1	1	yes	characteristic
43	C₄×D₄×C₁₃₁	C₂×C₄	1	2	yes	—
44	C₄×D₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
45	C₄×D₄×C₁₃₁	Q₈	1	2	yes	—
46	C₄×D₄×C₁₃₁	Q₈	1	1	yes	characteristic
47	#117×C₁₃₁	D₄	1	1	yes	characteristic
48	#117×C₁₃₁	D₄	1	2	yes	—
49	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
50	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
51	C₄⋊C₈×C₁₃₁	—	2	2	no	—
52	C₄⋊C₈×C₁₃₁	—	2	2	no	—
53	C₄⋊C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
54	C₄⋊C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
55	C₄⋊C₈×C₁₃₁	C₂×C₄	1	2	yes	—
56	C₄⋊C₈×C₁₃₁	C₂×C₄	1	2	yes	—
57	C₄⋊C₈×C₁₃₁	C₂³	1	2	yes	—
58	C₄⋊C₈×C₁₃₁	C₂³	1	2	yes	—
59	C₄⋊C₈×C₁₃₁	C₂³	1	4	yes	—
60	C₂²⋊C₈×C₁₃₁	—	2	4	no	—
61	C₂²⋊C₈×C₁₃₁	—	2	4	no	—
62	C₂²⋊C₈×C₁₃₁	C₂×C₄	1	2	yes	—
63	C₂²⋊C₈×C₁₃₁	C₂×C₄	1	2	yes	—
64	C₂²⋊C₈×C₁₃₁	C₂×C₄	1	2	yes	—
65	#97×C₁₃₁	—	2	4	no	—
66	C₄×C₈×C₁₃₁	—	2	4	no	—
67	C₄×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
68	C₄×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
69	C₄×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
70	C₄×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
71	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
72	C₄×C₈×C₁₃₁	C₂³	1	2	yes	—
73	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
74	#41×C₁₃₁	—	2	2	no	—
75	#41×C₁₃₁	—	2	2	no	—
76	C₂×Q₈×C₁₃₁	C₄⋊C₄	1	1	yes	characteristic
77	C₂×D₄×C₁₃₁	C₄⋊C₄	1	2	yes	—
78	C₂×D₄×C₁₃₁	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
82	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃₁	C₂×Q₈	1	2	yes	—
84	C₂²×C₄×C₁₃₁	C₂×Q₈	1	1	yes	characteristic
85	M₁₆×C₁₃₁	—	4	4	no	—
86	C₂×C₈×C₁₃₁	—	2	2	no	—
87	C₂×C₈×C₁₃₁	—	2	4	no	—
88	C₂×C₈×C₁₃₁	—	2	2	no	—
89	C₂×C₈×C₁₃₁	—	2	4	no	—
90	C₂×C₈×C₁₃₁	—	2	2	no	—
91	C₂×C₈×C₁₃₁	—	4	1	no	—
92	C₂×C₈×C₁₃₁	—	4	2	no	—
93	C₂×C₈×C₁₃₁	—	4	4	no	—
94	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
96	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
100	C₄⋊C₄×C₁₃₁	C₄⋊C₄	1	2	yes	—
101	C₄⋊C₄×C₁₃₁	C₄⋊C₄	1	1	yes	characteristic
102	C₄⋊C₄×C₁₃₁	C₄⋊C₄	1	2	yes	—
103	C₄⋊C₄×C₁₃₁	C₄⋊C₄	1	1	yes	characteristic
104	C₂²⋊C₄×C₁₃₁	C₄⋊C₄	1	2	yes	—
105	C₂²⋊C₄×C₁₃₁	C₄⋊C₄	1	2	yes	—
106	C₂²⋊C₄×C₁₃₁	C₄⋊C₄	1	2	yes	—
107	C₄²×C₁₃₁	C₂²×C₄	1	2	yes	—
108	C₄²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
110	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₁₃₁	C₂×Q₈	1	2	yes	—
112	C₄²×C₁₃₁	C₂×Q₈	1	1	yes	characteristic
113	C₄²×C₁₃₁	C₂⁴	1	1	yes	characteristic
114	C₂³×C₁₃₁	C₂×C₄⋊C₄	1	2	yes	—
115	C₂³×C₁₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
116	Q₈×C₁₃₁	—	2	2	no	—
117	D₄×C₁₃₁	—	2	4	no	—
118	D₄×C₁₃₁	—	2	2	no	—
119	C₂×C₄×C₁₃₁	—	2	1	no	—
120	C₂×C₄×C₁₃₁	—	2	2	no	—
121	C₂×C₄×C₁₃₁	—	2	1	no	—
122	C₂×C₄×C₁₃₁	—	2	2	no	—
123	C₂×C₄×C₁₃₁	—	2	2	no	—
124	C₂×C₄×C₁₃₁	—	2	2	no	—
125	C₂×C₄×C₁₃₁	—	4	1	no	—
126	C₂×C₄×C₁₃₁	—	4	2	no	—
127	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	2	yes	—
128	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	2	yes	—
130	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	2	yes	—
131	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₃₁	#135	1	2	yes	—
134	C₂×C₄×C₁₃₁	#135	1	2	yes	—
135	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₄×C₁₃₁	C₂²×Q₈	1	1	yes	characteristic
138	C₈×C₁₃₁	—	2	2	no	—
139	C₈×C₁₃₁	—	2	1	no	—
140	C₈×C₁₃₁	—	2	1	no	—
141	C₈×C₁₃₁	—	2	2	no	—
142	C₈×C₁₃₁	—	2	1	no	—
143	C₈×C₁₃₁	—	4	2	no	—
144	C₈×C₁₃₁	—	4	2	no	—
145	C₈×C₁₃₁	—	4	4	no	—
146	C₈×C₁₃₁	#131	1	2	yes	—
147	C₂²×C₁₃₁	—	2	1	no	—
148	C₂²×C₁₃₁	—	2	1	no	—
149	C₂²×C₁₃₁	—	2	2	no	—
150	C₂²×C₁₃₁	—	2	2	no	—
151	C₂²×C₁₃₁	—	2	2	no	—
152	C₂²×C₁₃₁	#427	1	2	yes	—
153	C₂²×C₁₃₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
154	C₄×C₁₃₁	—	2	1	no	—
155	C₄×C₁₃₁	—	2	2	no	—
156	C₄×C₁₃₁	—	2	2	no	—
157	C₄×C₁₃₁	—	2	1	no	—
158	C₄×C₁₃₁	—	2	1	no	—
159	C₄×C₁₃₁	—	2	2	no	—
160	C₄×C₁₃₁	#427	1	2	yes	—
161	C₄×C₁₃₁	C₂×#131	1	1	yes	characteristic
162	C₄×C₁₃₁	#568	1	1	yes	characteristic
163	C₄×C₁₃₁	C₂×#135	1	1	yes	characteristic
164	C₄×C₁₃₁	C₂×#135	1	1	yes	characteristic
165	C₂×C₁₃₁	—	2	2	no	—
166	C₂×C₁₃₁	—	4	2	no	—
167	C₂×C₁₃₁	#2906	1	1	yes	characteristic
168	C₂×C₁₃₁	C₂×#427	1	1	yes	characteristic
169	C₂×C₁₃₁	#2916	1	1	yes	characteristic
170	#17829	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₁₃₁	#17829	1	1	yes	characteristic, direct product factor, Sylow
172	C₈×#41	C₂×C₁₃₁	1	1	yes	characteristic
173	#2925	C₂×C₁₃₁	1	2	yes	—
174	#1572	C₂×C₁₃₁	1	4	yes	complemented
175	#1570	C₂×C₁₃₁	1	2	yes	complemented
176	#1568	C₂×C₁₃₁	1	2	yes	complemented
177	#1567	C₂×C₁₃₁	1	1	yes	characteristic, complemented
178	#1564	C₂×C₁₃₁	1	2	yes	complemented
179	C₂×#335	C₂×C₁₃₁	1	1	yes	characteristic, complemented
180	C₄×#41	C₂²×C₁₃₁	1	1	yes	characteristic
181	C₈×Q₈	C₄×C₁₃₁	1	1	yes	characteristic
182	C₈×Q₈	C₄×C₁₃₁	1	1	yes	characteristic
183	C₈×D₄	C₄×C₁₃₁	1	1	yes	characteristic
184	C₈×D₄	C₄×C₁₃₁	1	2	yes	—
185	C₈×D₄	C₄×C₁₃₁	1	1	yes	characteristic
186	C₈×D₄	C₄×C₁₃₁	1	2	yes	—
187	#433	—	2	4	no	—
188	#432	C₂²×C₁₃₁	1	4	yes	—
189	#431	C₂²×C₁₃₁	1	4	yes	—
190	#431	C₂²×C₁₃₁	1	1	yes	characteristic
191	#431	C₂²×C₁₃₁	1	2	yes	—
192	#423	C₂²×C₁₃₁	1	2	yes	—
193	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
194	#408	—	2	2	no	—
195	#405	—	2	2	no	—
196	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
197	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	—
198	#335	C₂²×C₁₃₁	1	1	yes	characteristic
199	#335	C₂²×C₁₃₁	1	1	yes	characteristic
200	#335	C₂²×C₁₃₁	1	2	yes	—
201	#335	C₂²×C₁₃₁	1	2	yes	—
202	#335	C₂²×C₁₃₁	1	2	yes	—
203	#334	C₂²×C₁₃₁	1	4	yes	—
204	#334	C₂²×C₁₃₁	1	4	yes	—
205	C₂×#41	D₄×C₁₃₁	1	1	yes	characteristic
206	C₂×M₁₆	—	2	2	no	—
207	C₂²×C₈	—	2	2	no	—
208	C₂²×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
209	C₂²×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
210	C₂²×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
211	C₂²×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
212	C₄×Q₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
213	C₄×Q₈	Q₈×C₁₃₁	1	1	yes	characteristic
214	C₄×D₄	C₂×C₄×C₁₃₁	1	2	yes	—
215	C₄×D₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
216	C₄×D₄	Q₈×C₁₃₁	1	2	yes	—
217	C₄×D₄	Q₈×C₁₃₁	1	1	yes	characteristic
218	#117	D₄×C₁₃₁	1	1	yes	characteristic
219	#117	D₄×C₁₃₁	1	2	yes	—
220	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
221	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
222	C₄⋊C₈	—	2	2	no	—
223	C₄⋊C₈	—	2	2	no	—
224	C₄⋊C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
225	C₄⋊C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
226	C₄⋊C₈	C₂×C₄×C₁₃₁	1	2	yes	—
227	C₄⋊C₈	C₂×C₄×C₁₃₁	1	2	yes	—
228	C₄⋊C₈	C₂³×C₁₃₁	1	2	yes	—
229	C₄⋊C₈	C₂³×C₁₃₁	1	2	yes	—
230	C₄⋊C₈	C₂³×C₁₃₁	1	4	yes	—
231	C₂²⋊C₈	—	2	4	no	—
232	C₂²⋊C₈	—	2	4	no	—
233	C₂²⋊C₈	C₂×C₄×C₁₃₁	1	2	yes	—
234	C₂²⋊C₈	C₂×C₄×C₁₃₁	1	2	yes	—
235	C₂²⋊C₈	C₂×C₄×C₁₃₁	1	2	yes	—
236	#97	—	2	4	no	—
237	C₄×C₈	—	2	4	no	—
238	C₄×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
239	C₄×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
240	C₄×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
241	C₄×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
242	C₄×C₈	C₂³×C₁₃₁	1	2	yes	—
243	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
244	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
245	#41	—	2	2	no	—
246	#41	—	2	2	no	—
247	C₂×Q₈	C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
248	C₂×D₄	C₄⋊C₄×C₁₃₁	1	2	yes	—
249	C₂×D₄	C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
250	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
251	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
252	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
253	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
254	C₂²×C₄	C₂×Q₈×C₁₃₁	1	2	yes	—
255	C₂²×C₄	C₂×Q₈×C₁₃₁	1	1	yes	characteristic
256	M₁₆	—	4	4	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	4	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	4	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	4	1	no	—
263	C₂×C₈	—	4	2	no	—
264	C₂×C₈	—	4	4	no	—
265	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
266	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
267	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
268	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
269	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
270	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
271	C₄⋊C₄	C₄⋊C₄×C₁₃₁	1	2	yes	—
272	C₄⋊C₄	C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
273	C₄⋊C₄	C₄⋊C₄×C₁₃₁	1	2	yes	—
274	C₄⋊C₄	C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
275	C₂²⋊C₄	C₄⋊C₄×C₁₃₁	1	2	yes	—
276	C₂²⋊C₄	C₄⋊C₄×C₁₃₁	1	2	yes	—
277	C₂²⋊C₄	C₄⋊C₄×C₁₃₁	1	2	yes	—
278	C₄²	C₂²×C₄×C₁₃₁	1	2	yes	—
279	C₄²	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
280	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
281	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
282	C₄²	C₂×Q₈×C₁₃₁	1	2	yes	—
283	C₄²	C₂×Q₈×C₁₃₁	1	1	yes	characteristic
284	C₄²	C₂⁴×C₁₃₁	1	1	yes	characteristic
285	C₂³	C₂×C₄⋊C₄×C₁₃₁	1	2	yes	—
286	C₂³	C₂×C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
287	Q₈	—	2	2	no	—
288	D₄	—	2	4	no	—
289	D₄	—	2	2	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	4	1	no	—
297	C₂×C₄	—	4	2	no	—
298	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	2	yes	—
299	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
300	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	2	yes	—
301	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	2	yes	—
302	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
303	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
304	C₂×C₄	#135×C₁₃₁	1	2	yes	—
305	C₂×C₄	#135×C₁₃₁	1	2	yes	—
306	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
307	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
308	C₂×C₄	C₂²×Q₈×C₁₃₁	1	1	yes	characteristic
309	C₈	—	2	2	no	—
310	C₈	—	2	1	no	—
311	C₈	—	2	1	no	—
312	C₈	—	2	2	no	—
313	C₈	—	2	1	no	—
314	C₈	—	4	2	no	—
315	C₈	—	4	2	no	—
316	C₈	—	4	4	no	—
317	C₈	#131×C₁₃₁	1	2	yes	—
318	C₂²	—	2	1	no	—
319	C₂²	—	2	1	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	2	2	no	—
323	C₂²	#427×C₁₃₁	1	2	yes	—
324	C₂²	C₂²×C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
325	C₄	—	2	1	no	—
326	C₄	—	2	2	no	—
327	C₄	—	2	2	no	—
328	C₄	—	2	1	no	—
329	C₄	—	2	1	no	—
330	C₄	—	2	2	no	—
331	C₄	#427×C₁₃₁	1	2	yes	—
332	C₄	C₂×#131×C₁₃₁	1	1	yes	characteristic
333	C₄	#568×C₁₃₁	1	1	yes	characteristic
334	C₄	C₂×#135×C₁₃₁	1	1	yes	characteristic
335	C₄	C₂×#135×C₁₃₁	1	1	yes	characteristic
336	C₂	—	2	2	no	—
337	C₂	—	4	2	no	—
338	C₂	#2906×C₁₃₁	1	1	yes	characteristic
339	C₂	C₂×#427×C₁₃₁	1	1	yes	characteristic
340	C₂	#2916×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₄²	C₂⁴×C₁₃₁
socle	C₂²×C₁₃₁	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₁₃₁	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₁ ◁ C₄×#41×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. #1572×C₁₃₁	C₂	semidirect
4. #1570×C₁₃₁	C₂	semidirect
5. #1568×C₁₃₁	C₂	semidirect
6. #1567×C₁₃₁	C₂	semidirect
7. #1564×C₁₃₁	C₂	semidirect
8. C₂×#335×C₁₃₁	C₂	semidirect
170. #17829	C₁₃₁	direct (N × H)
171. C₁₃₁	#17829	direct (N × H)
174. #1572	C₂×C₁₃₁	semidirect
175. #1570	C₂×C₁₃₁	semidirect
176. #1568	C₂×C₁₃₁	semidirect
177. #1567	C₂×C₁₃₁	semidirect
178. #1564	C₂×C₁₃₁	semidirect
179. C₂×#335	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₈×#41×C₁₃₁	2
#2925×C₁₃₁	2
#1572×C₁₃₁	2
#1570×C₁₃₁	2
#1568×C₁₃₁	2
#1567×C₁₃₁	2
#1564×C₁₃₁	2
C₂×#335×C₁₃₁	2
#17829	131

Subgroups — C131×#17829 #45703713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#17829 #45703713