Subgroups — C₁₃₁×#22804 #45708688

Order 33536.

710 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2943×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2925×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#1975×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#1974×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	#1929×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1929×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#1849×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1806×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#1773×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1772×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1771×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₄×#41×C₁₃₁	C₂²	1	2	yes	—
14	#442×C₁₃₁	C₄	1	2	yes	complemented
15	#441×C₁₃₁	C₄	1	2	yes	complemented
16	#440×C₁₃₁	C₄	1	2	yes	complemented
17	#440×C₁₃₁	C₄	1	2	yes	complemented
18	#433×C₁₃₁	—	2	2	no	—
19	#433×C₁₃₁	—	2	2	no	—
20	#432×C₁₃₁	—	2	2	no	—
21	#431×C₁₃₁	—	2	2	no	—
22	C₂×#108×C₁₃₁	C₂²	1	1	yes	characteristic
23	C₂×#108×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₂×#108×C₁₃₁	C₂²	1	2	yes	—
25	#427×C₁₃₁	C₂²	1	1	yes	characteristic
26	#423×C₁₃₁	C₂²	1	2	yes	—
27	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂×#104×C₁₃₁	C₂²	1	2	yes	—
29	C₂×#104×C₁₃₁	C₂²	1	2	yes	—
30	#416×C₁₃₁	C₂²	1	2	yes	—
31	#408×C₁₃₁	C₂²	1	2	yes	—
32	#408×C₁₃₁	C₂²	1	2	yes	—
33	#405×C₁₃₁	C₂²	1	2	yes	—
34	#405×C₁₃₁	C₂²	1	2	yes	—
35	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
36	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
39	#339×C₁₃₁	C₂²	1	2	yes	—
40	#339×C₁₃₁	C₂²	1	2	yes	—
41	#336×C₁₃₁	C₂²	1	1	yes	characteristic
42	#336×C₁₃₁	C₂²	1	1	yes	characteristic
43	C₂×#41×C₁₃₁	C₂³	1	2	yes	—
44	#135×C₁₃₁	—	2	2	no	—
45	#135×C₁₃₁	—	2	2	no	—
46	C₂×Q₁₆×C₁₃₁	C₂×C₄	1	1	yes	characteristic
47	C₂×SD₁₆×C₁₃₁	C₂×C₄	1	2	yes	—
48	C₂×D₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
49	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
50	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
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	C₂×C₄	1	2	yes	—
56	C₄×Q₈×C₁₃₁	C₂×C₄	1	2	yes	—
57	C₄×D₄×C₁₃₁	—	2	2	no	—
58	C₄×D₄×C₁₃₁	—	2	2	no	—
59	C₄×D₄×C₁₃₁	C₂×C₄	1	2	yes	—
60	C₄×D₄×C₁₃₁	C₂×C₄	1	2	yes	—
61	#117×C₁₃₁	—	2	2	no	—
62	#117×C₁₃₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
64	C₂×C₄²×C₁₃₁	—	2	2	no	—
65	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
68	#108×C₁₃₁	—	2	2	no	—
69	#108×C₁₃₁	—	2	2	no	—
70	#108×C₁₃₁	—	4	2	no	—
71	#107×C₁₃₁	C₂×C₄	1	1	yes	characteristic
72	#107×C₁₃₁	C₂×C₄	1	1	yes	characteristic
73	#106×C₁₃₁	C₂×C₄	1	2	yes	—
74	C₄⋊C₈×C₁₃₁	—	2	2	no	—
75	C₄⋊C₈×C₁₃₁	—	2	2	no	—
76	C₄⋊C₈×C₁₃₁	D₄	1	2	yes	—
77	C₄⋊C₈×C₁₃₁	D₄	1	2	yes	—
78	#104×C₁₃₁	—	4	2	no	—
79	#104×C₁₃₁	—	4	2	no	—
80	#103×C₁₃₁	C₂×C₄	1	2	yes	—
81	#103×C₁₃₁	C₂×C₄	1	2	yes	—
82	#102×C₁₃₁	C₂×C₄	1	2	yes	—
83	#102×C₁₃₁	C₂×C₄	1	2	yes	—
84	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
85	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
86	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
87	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
88	#97×C₁₃₁	—	2	2	no	—
89	#97×C₁₃₁	—	2	2	no	—
90	#97×C₁₃₁	—	2	2	no	—
91	#97×C₁₃₁	C₂×C₄	1	2	yes	—
92	#97×C₁₃₁	C₂×C₄	1	2	yes	—
93	C₄×C₈×C₁₃₁	—	2	2	no	—
94	C₄×C₈×C₁₃₁	—	2	2	no	—
95	C₄×C₈×C₁₃₁	—	2	2	no	—
96	#95×C₁₃₁	—	2	1	no	—
97	#41×C₁₃₁	—	2	2	no	—
98	#41×C₁₃₁	—	2	2	no	—
99	#41×C₁₃₁	—	2	2	no	—
100	#41×C₁₃₁	—	2	2	no	—
101	C₂×Q₈×C₁₃₁	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₁₃₁	—	2	2	no	—
103	C₂×D₄×C₁₃₁	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₃₁	—	2	1	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	1	no	—
109	C₂²×C₄×C₁₃₁	#41	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₁	#41	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
112	Q₁₆×C₁₃₁	—	2	2	no	—
113	SD₁₆×C₁₃₁	—	2	4	no	—
114	D₈×C₁₃₁	—	2	2	no	—
115	M₁₆×C₁₃₁	—	2	2	no	—
116	M₁₆×C₁₃₁	—	2	2	no	—
117	M₁₆×C₁₃₁	—	2	2	no	—
118	M₁₆×C₁₃₁	—	2	2	no	—
119	C₂×C₈×C₁₃₁	—	2	1	no	—
120	C₂×C₈×C₁₃₁	—	2	1	no	—
121	C₂×C₈×C₁₃₁	—	2	1	no	—
122	C₂×C₈×C₁₃₁	—	2	1	no	—
123	C₂×C₈×C₁₃₁	—	2	1	no	—
124	C₂×C₈×C₁₃₁	—	2	1	no	—
125	C₂×C₈×C₁₃₁	—	2	2	no	—
126	C₂×C₈×C₁₃₁	—	2	2	no	—
127	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃₁	#41	1	2	yes	—
134	C₂×C₈×C₁₃₁	#41	1	2	yes	—
135	C₄⋊C₄×C₁₃₁	—	2	2	no	—
136	C₄⋊C₄×C₁₃₁	—	2	2	no	—
137	C₄⋊C₄×C₁₃₁	—	4	2	no	—
138	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
139	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
140	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
141	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
142	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
143	C₄²×C₁₃₁	—	2	2	no	—
144	C₄²×C₁₃₁	—	2	2	no	—
145	C₄²×C₁₃₁	—	2	2	no	—
146	C₄²×C₁₃₁	—	2	1	no	—
147	C₄²×C₁₃₁	—	2	1	no	—
148	C₄²×C₁₃₁	—	2	1	no	—
149	C₄²×C₁₃₁	—	2	1	no	—
150	C₄²×C₁₃₁	C₂²×C₄	1	2	yes	—
151	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
152	C₂³×C₁₃₁	—	2	2	no	—
153	C₂³×C₁₃₁	C₂×#41	1	1	yes	characteristic
154	Q₈×C₁₃₁	—	2	2	no	—
155	Q₈×C₁₃₁	—	2	2	no	—
156	D₄×C₁₃₁	—	2	2	no	—
157	D₄×C₁₃₁	—	2	2	no	—
158	D₄×C₁₃₁	—	4	2	no	—
159	D₄×C₁₃₁	—	4	2	no	—
160	C₂×C₄×C₁₃₁	—	2	2	no	—
161	C₂×C₄×C₁₃₁	—	2	2	no	—
162	C₂×C₄×C₁₃₁	—	2	2	no	—
163	C₂×C₄×C₁₃₁	—	2	2	no	—
164	C₂×C₄×C₁₃₁	—	4	1	no	—
165	C₂×C₄×C₁₃₁	—	4	1	no	—
166	C₂×C₄×C₁₃₁	—	4	4	no	—
167	C₂×C₄×C₁₃₁	—	4	1	no	—
168	C₂×C₄×C₁₃₁	—	4	1	no	—
169	C₂×C₄×C₁₃₁	—	4	2	no	—
170	C₂×C₄×C₁₃₁	—	4	2	no	—
171	C₂×C₄×C₁₃₁	—	4	1	no	—
172	C₂×C₄×C₁₃₁	—	4	1	no	—
173	C₂×C₄×C₁₃₁	—	4	1	no	—
174	C₂×C₄×C₁₃₁	—	8	2	no	—
175	C₂×C₄×C₁₃₁	C₄×D₄	1	2	yes	—
176	C₂×C₄×C₁₃₁	C₄×D₄	1	2	yes	—
177	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
183	C₈×C₁₃₁	—	2	2	no	—
184	C₈×C₁₃₁	—	2	1	no	—
185	C₈×C₁₃₁	—	2	1	no	—
186	C₈×C₁₃₁	—	2	2	no	—
187	C₈×C₁₃₁	—	4	2	no	—
188	C₈×C₁₃₁	—	4	2	no	—
189	C₈×C₁₃₁	#117	1	2	yes	—
190	C₈×C₁₃₁	#117	1	2	yes	—
191	C₂²×C₁₃₁	—	2	1	no	—
192	C₂²×C₁₃₁	—	2	1	no	—
193	C₂²×C₁₃₁	—	4	2	no	—
194	C₂²×C₁₃₁	—	4	2	no	—
195	C₂²×C₁₃₁	—	4	2	no	—
196	C₂²×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
197	C₂²×C₁₃₁	#555	1	1	yes	characteristic
198	C₂²×C₁₃₁	#556	1	1	yes	characteristic
199	C₄×C₁₃₁	—	2	2	no	—
200	C₄×C₁₃₁	—	2	2	no	—
201	C₄×C₁₃₁	—	4	2	no	—
202	C₄×C₁₃₁	—	4	2	no	—
203	C₄×C₁₃₁	—	4	2	no	—
204	C₄×C₁₃₁	—	4	2	no	—
205	C₄×C₁₃₁	—	8	1	no	—
206	C₄×C₁₃₁	C₂×#117	1	1	yes	characteristic
207	C₄×C₁₃₁	#520	1	1	yes	characteristic
208	C₄×C₁₃₁	#547	1	1	yes	characteristic
209	C₄×C₁₃₁	#550	1	1	yes	characteristic
210	C₂×C₁₃₁	—	2	1	no	—
211	C₂×C₁₃₁	—	2	1	no	—
212	C₂×C₁₃₁	—	8	2	no	—
213	C₂×C₁₃₁	#2354	1	1	yes	characteristic
214	C₂×C₁₃₁	#2955	1	1	yes	characteristic
215	C₂×C₁₃₁	#2956	1	1	yes	characteristic
216	#22804	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₁₃₁	#22804	1	1	yes	characteristic, direct product factor, Sylow
218	#2943	C₂×C₁₃₁	1	1	yes	characteristic
219	#2925	C₂×C₁₃₁	1	2	yes	complemented
220	#1975	C₂×C₁₃₁	1	1	yes	characteristic
221	#1974	C₂×C₁₃₁	1	1	yes	characteristic
222	#1929	C₂×C₁₃₁	1	2	yes	complemented
223	#1929	C₂×C₁₃₁	1	2	yes	complemented
224	#1849	C₂×C₁₃₁	1	1	yes	characteristic, complemented
225	#1806	C₂×C₁₃₁	1	2	yes	complemented
226	#1773	C₂×C₁₃₁	1	1	yes	characteristic, complemented
227	#1772	C₂×C₁₃₁	1	1	yes	characteristic, complemented
228	#1771	C₂×C₁₃₁	1	1	yes	characteristic, complemented
229	C₂×#135	C₂²×C₁₃₁	1	1	yes	characteristic
230	C₄×#41	C₂²×C₁₃₁	1	2	yes	—
231	#442	C₄×C₁₃₁	1	2	yes	complemented
232	#441	C₄×C₁₃₁	1	2	yes	complemented
233	#440	C₄×C₁₃₁	1	2	yes	complemented
234	#440	C₄×C₁₃₁	1	2	yes	complemented
235	#433	—	2	2	no	—
236	#433	—	2	2	no	—
237	#432	—	2	2	no	—
238	#431	—	2	2	no	—
239	C₂×#108	C₂²×C₁₃₁	1	1	yes	characteristic
240	C₂×#108	C₂²×C₁₃₁	1	1	yes	characteristic
241	C₂×#108	C₂²×C₁₃₁	1	2	yes	—
242	#427	C₂²×C₁₃₁	1	1	yes	characteristic
243	#423	C₂²×C₁₃₁	1	2	yes	—
244	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
245	C₂×#104	C₂²×C₁₃₁	1	2	yes	—
246	C₂×#104	C₂²×C₁₃₁	1	2	yes	—
247	#416	C₂²×C₁₃₁	1	2	yes	—
248	#408	C₂²×C₁₃₁	1	2	yes	—
249	#408	C₂²×C₁₃₁	1	2	yes	—
250	#405	C₂²×C₁₃₁	1	2	yes	—
251	#405	C₂²×C₁₃₁	1	2	yes	—
252	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
253	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
254	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
255	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
256	#339	C₂²×C₁₃₁	1	2	yes	—
257	#339	C₂²×C₁₃₁	1	2	yes	—
258	#336	C₂²×C₁₃₁	1	1	yes	characteristic
259	#336	C₂²×C₁₃₁	1	1	yes	characteristic
260	C₂×#41	C₂³×C₁₃₁	1	2	yes	—
261	#135	—	2	2	no	—
262	#135	—	2	2	no	—
263	C₂×Q₁₆	C₂×C₄×C₁₃₁	1	1	yes	characteristic
264	C₂×SD₁₆	C₂×C₄×C₁₃₁	1	2	yes	—
265	C₂×D₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
266	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
267	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
268	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
272	C₄×Q₈	C₂×C₄×C₁₃₁	1	2	yes	—
273	C₄×Q₈	C₂×C₄×C₁₃₁	1	2	yes	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	C₂×C₄×C₁₃₁	1	2	yes	—
277	C₄×D₄	C₂×C₄×C₁₃₁	1	2	yes	—
278	#117	—	2	2	no	—
279	#117	C₂³×C₁₃₁	1	2	yes	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄²	—	2	2	no	—
282	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
284	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
285	#108	—	2	2	no	—
286	#108	—	2	2	no	—
287	#108	—	4	2	no	—
288	#107	C₂×C₄×C₁₃₁	1	1	yes	characteristic
289	#107	C₂×C₄×C₁₃₁	1	1	yes	characteristic
290	#106	C₂×C₄×C₁₃₁	1	2	yes	—
291	C₄⋊C₈	—	2	2	no	—
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	D₄×C₁₃₁	1	2	yes	—
294	C₄⋊C₈	D₄×C₁₃₁	1	2	yes	—
295	#104	—	4	2	no	—
296	#104	—	4	2	no	—
297	#103	C₂×C₄×C₁₃₁	1	2	yes	—
298	#103	C₂×C₄×C₁₃₁	1	2	yes	—
299	#102	C₂×C₄×C₁₃₁	1	2	yes	—
300	#102	C₂×C₄×C₁₃₁	1	2	yes	—
301	C₂²⋊C₈	—	2	2	no	—
302	C₂²⋊C₈	—	2	2	no	—
303	C₂²⋊C₈	—	2	2	no	—
304	C₂²⋊C₈	—	2	2	no	—
305	#97	—	2	2	no	—
306	#97	—	2	2	no	—
307	#97	—	2	2	no	—
308	#97	C₂×C₄×C₁₃₁	1	2	yes	—
309	#97	C₂×C₄×C₁₃₁	1	2	yes	—
310	C₄×C₈	—	2	2	no	—
311	C₄×C₈	—	2	2	no	—
312	C₄×C₈	—	2	2	no	—
313	#95	—	2	1	no	—
314	#41	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	#41	—	2	2	no	—
318	C₂×Q₈	C₂²×C₄×C₁₃₁	1	2	yes	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	C₂²×C₄×C₁₃₁	1	2	yes	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	#41×C₁₃₁	1	1	yes	characteristic
327	C₂²×C₄	#41×C₁₃₁	1	1	yes	characteristic
328	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
329	Q₁₆	—	2	2	no	—
330	SD₁₆	—	2	4	no	—
331	D₈	—	2	2	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	2	2	no	—
334	M₁₆	—	2	2	no	—
335	M₁₆	—	2	2	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
345	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
346	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
347	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
348	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
349	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
350	C₂×C₈	#41×C₁₃₁	1	2	yes	—
351	C₂×C₈	#41×C₁₃₁	1	2	yes	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
356	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₄²	C₂²×C₄×C₁₃₁	1	2	yes	—
368	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
369	C₂³	—	2	2	no	—
370	C₂³	C₂×#41×C₁₃₁	1	1	yes	characteristic
371	Q₈	—	2	2	no	—
372	Q₈	—	2	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	2	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	8	2	no	—
392	C₂×C₄	C₄×D₄×C₁₃₁	1	2	yes	—
393	C₂×C₄	C₄×D₄×C₁₃₁	1	2	yes	—
394	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
396	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
397	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
398	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
399	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
400	C₈	—	2	2	no	—
401	C₈	—	2	1	no	—
402	C₈	—	2	1	no	—
403	C₈	—	2	2	no	—
404	C₈	—	4	2	no	—
405	C₈	—	4	2	no	—
406	C₈	#117×C₁₃₁	1	2	yes	—
407	C₈	#117×C₁₃₁	1	2	yes	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
414	C₂²	#555×C₁₃₁	1	1	yes	characteristic
415	C₂²	#556×C₁₃₁	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	8	1	no	—
423	C₄	C₂×#117×C₁₃₁	1	1	yes	characteristic
424	C₄	#520×C₁₃₁	1	1	yes	characteristic
425	C₄	#547×C₁₃₁	1	1	yes	characteristic
426	C₄	#550×C₁₃₁	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	8	2	no	—
430	C₂	#2354×C₁₃₁	1	1	yes	characteristic
431	C₂	#2955×C₁₃₁	1	1	yes	characteristic
432	C₂	#2956×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
socle	C₂²×C₁₃₁	C₂×C₄×D₄
prime radical	C₂×#135×C₁₃₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₁ ◁ C₂×C₄⋊C₈×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2925×C₁₃₁	C₂	semidirect
5. #1929×C₁₃₁	C₂	semidirect
6. #1929×C₁₃₁	C₂	semidirect
7. #1849×C₁₃₁	C₂	semidirect
8. #1806×C₁₃₁	C₂	semidirect
9. #1773×C₁₃₁	C₂	semidirect
10. #1772×C₁₃₁	C₂	semidirect
11. #1771×C₁₃₁	C₂	semidirect
14. #442×C₁₃₁	C₄	semidirect
15. #441×C₁₃₁	C₄	semidirect
16. #440×C₁₃₁	C₄	semidirect
17. #440×C₁₃₁	C₄	semidirect
216. #22804	C₁₃₁	direct (N × H)
217. C₁₃₁	#22804	direct (N × H)
219. #2925	C₂×C₁₃₁	semidirect
222. #1929	C₂×C₁₃₁	semidirect
223. #1929	C₂×C₁₃₁	semidirect
224. #1849	C₂×C₁₃₁	semidirect
225. #1806	C₂×C₁₃₁	semidirect
226. #1773	C₂×C₁₃₁	semidirect
227. #1772	C₂×C₁₃₁	semidirect
228. #1771	C₂×C₁₃₁	semidirect
231. #442	C₄×C₁₃₁	semidirect
232. #441	C₄×C₁₃₁	semidirect
233. #440	C₄×C₁₃₁	semidirect
234. #440	C₄×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#2943×C₁₃₁	2
#2925×C₁₃₁	2
#1975×C₁₃₁	2
#1974×C₁₃₁	2
#1929×C₁₃₁	2
#1849×C₁₃₁	2
#1806×C₁₃₁	2
#1773×C₁₃₁	2
#1772×C₁₃₁	2
#1771×C₁₃₁	2
#22804	131

Subgroups — C131×#22804 #45708688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#22804 #45708688