Subgroups — C₁₅₁×#21545 #50326470

Order 38656.

906 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3050×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#443×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2930×C₁₅₁	C₂	1	2	yes	maximal, complemented
4	C₂×#405×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#1974×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#1945×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1938×C₁₅₁	C₂	1	2	yes	maximal, complemented
8	#1897×C₁₅₁	C₂	1	2	yes	maximal, complemented
9	#1810×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1772×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1765×C₁₅₁	C₂	1	2	yes	maximal, complemented
12	C₂×#135×C₁₅₁	C₂²	1	1	yes	characteristic
13	C₂×#131×C₁₅₁	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
16	#525×C₁₅₁	C₂²	1	2	yes	—
17	C₂×#117×C₁₅₁	C₂²	1	1	yes	characteristic
18	#467×C₁₅₁	C₄	1	2	yes	complemented
19	#466×C₁₅₁	C₄	1	2	yes	complemented
20	#465×C₁₅₁	C₄	1	4	yes	complemented
21	#443×C₁₅₁	—	2	4	no	—
22	#436×C₁₅₁	—	2	4	no	—
23	#435×C₁₅₁	—	2	4	no	—
24	C₂×#108×C₁₅₁	C₂²	1	1	yes	characteristic
25	C₂×#108×C₁₅₁	C₂²	1	1	yes	characteristic
26	#427×C₁₅₁	C₂²	1	1	yes	characteristic
27	#424×C₁₅₁	C₂²	1	2	yes	—
28	C₂×#104×C₁₅₁	C₂²	1	2	yes	—
29	C₂×#104×C₁₅₁	C₂²	1	2	yes	—
30	#416×C₁₅₁	C₂²	1	2	yes	—
31	#408×C₁₅₁	C₂²	1	2	yes	—
32	#407×C₁₅₁	C₂²	1	2	yes	—
33	#405×C₁₅₁	—	2	4	no	—
34	#405×C₁₅₁	C₂²	1	2	yes	—
35	C₂×#97×C₁₅₁	C₂²	1	1	yes	characteristic
36	C₂×#97×C₁₅₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
39	#341×C₁₅₁	C₂²	1	2	yes	—
40	#339×C₁₅₁	C₂²	1	2	yes	—
41	#339×C₁₅₁	C₂²	1	2	yes	—
42	C₂×#41×C₁₅₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
44	#135×C₁₅₁	—	2	2	no	—
45	#135×C₁₅₁	—	2	2	no	—
46	C₂×Q₁₆×C₁₅₁	C₂×C₄	1	1	yes	characteristic
47	C₂×SD₁₆×C₁₅₁	C₂×C₄	1	2	yes	—
48	C₂×D₈×C₁₅₁	C₂×C₄	1	1	yes	characteristic
49	#131×C₁₅₁	—	2	4	no	—
50	#131×C₁₅₁	—	2	4	no	—
51	C₂×M₁₆×C₁₅₁	—	2	2	no	—
52	C₂×M₁₆×C₁₅₁	—	2	2	no	—
53	C₂×M₁₆×C₁₅₁	—	2	2	no	—
54	C₂×M₁₆×C₁₅₁	D₄	1	2	yes	—
55	C₂×M₁₆×C₁₅₁	D₄	1	2	yes	—
56	C₂×M₁₆×C₁₅₁	C₂³	1	2	yes	—
57	C₂×M₁₆×C₁₅₁	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₅₁	—	2	2	no	—
59	C₂²×C₈×C₁₅₁	—	2	2	no	—
60	C₂²×C₈×C₁₅₁	—	2	2	no	—
61	C₂²×C₈×C₁₅₁	C₂×C₄	1	2	yes	—
62	C₂²×C₈×C₁₅₁	C₂×C₄	1	2	yes	—
63	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
67	#123×C₁₅₁	—	2	2	no	—
68	C₂²⋊Q₈×C₁₅₁	C₂×C₄	1	4	yes	—
69	#121×C₁₅₁	C₂×C₄	1	4	yes	—
70	#120×C₁₅₁	—	2	2	no	—
71	C₄×D₄×C₁₅₁	—	2	4	no	—
72	#117×C₁₅₁	—	2	2	no	—
73	#117×C₁₅₁	—	2	2	no	—
74	#117×C₁₅₁	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₅₁	—	2	1	no	—
77	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
79	#108×C₁₅₁	—	2	2	no	—
80	#108×C₁₅₁	—	2	2	no	—
81	#107×C₁₅₁	C₂×C₄	1	2	yes	—
82	#106×C₁₅₁	C₂×C₄	1	2	yes	—
83	C₄⋊C₈×C₁₅₁	—	2	4	no	—
84	#104×C₁₅₁	—	2	4	no	—
85	#104×C₁₅₁	—	2	4	no	—
86	#103×C₁₅₁	C₂×C₄	1	4	yes	—
87	#102×C₁₅₁	C₂×C₄	1	4	yes	—
88	C₂²⋊C₈×C₁₅₁	—	2	4	no	—
89	C₂²⋊C₈×C₁₅₁	—	2	4	no	—
90	#97×C₁₅₁	—	2	2	no	—
91	#97×C₁₅₁	—	2	2	no	—
92	#97×C₁₅₁	—	2	2	no	—
93	C₄×C₈×C₁₅₁	—	2	2	no	—
94	C₄×C₈×C₁₅₁	—	2	2	no	—
95	C₄×C₈×C₁₅₁	D₄	1	4	yes	complemented
96	C₂⁴×C₁₅₁	#41	1	1	yes	characteristic
97	#41×C₁₅₁	—	2	2	no	—
98	#41×C₁₅₁	—	2	2	no	—
99	#41×C₁₅₁	—	2	2	no	—
100	#41×C₁₅₁	—	2	2	no	—
101	C₂×Q₈×C₁₅₁	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₁₅₁	—	2	2	no	—
103	C₂×D₄×C₁₅₁	—	2	4	no	—
104	C₂×D₄×C₁₅₁	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₅₁	—	2	1	no	—
106	C₂²×C₄×C₁₅₁	—	2	1	no	—
107	C₂²×C₄×C₁₅₁	—	2	1	no	—
108	C₂²×C₄×C₁₅₁	—	2	1	no	—
109	C₂²×C₄×C₁₅₁	—	2	1	no	—
110	C₂²×C₄×C₁₅₁	—	2	1	no	—
111	C₂²×C₄×C₁₅₁	—	2	2	no	—
112	C₂²×C₄×C₁₅₁	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₅₁	#41	1	1	yes	characteristic
115	C₂²×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
116	Q₁₆×C₁₅₁	—	2	2	no	—
117	SD₁₆×C₁₅₁	—	2	4	no	—
118	D₈×C₁₅₁	—	2	2	no	—
119	M₁₆×C₁₅₁	—	2	4	no	—
120	M₁₆×C₁₅₁	—	2	4	no	—
121	M₁₆×C₁₅₁	—	2	2	no	—
122	M₁₆×C₁₅₁	—	2	2	no	—
123	M₁₆×C₁₅₁	—	2	2	no	—
124	M₁₆×C₁₅₁	—	2	2	no	—
125	M₁₆×C₁₅₁	—	4	4	no	—
126	C₂×C₈×C₁₅₁	—	2	1	no	—
127	C₂×C₈×C₁₅₁	—	2	1	no	—
128	C₂×C₈×C₁₅₁	—	2	1	no	—
129	C₂×C₈×C₁₅₁	—	2	1	no	—
130	C₂×C₈×C₁₅₁	—	2	4	no	—
131	C₂×C₈×C₁₅₁	—	2	4	no	—
132	C₂×C₈×C₁₅₁	—	2	2	no	—
133	C₂×C₈×C₁₅₁	—	2	2	no	—
134	C₂×C₈×C₁₅₁	—	4	4	no	—
135	C₂×C₈×C₁₅₁	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₁₅₁	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₁₅₁	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₁₅₁	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₅₁	#41	1	2	yes	—
144	C₂×C₈×C₁₅₁	#41	1	2	yes	—
145	C₄⋊C₄×C₁₅₁	—	2	4	no	—
146	C₄⋊C₄×C₁₅₁	—	2	4	no	—
147	C₄⋊C₄×C₁₅₁	C₂²×C₄	1	4	yes	—
148	C₂²⋊C₄×C₁₅₁	—	2	4	no	—
149	C₂²⋊C₄×C₁₅₁	—	2	4	no	—
150	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
151	C₂²⋊C₄×C₁₅₁	—	2	4	no	—
152	C₄²×C₁₅₁	—	2	1	no	—
153	C₄²×C₁₅₁	—	2	2	no	—
154	C₄²×C₁₅₁	—	2	1	no	—
155	C₄²×C₁₅₁	C₂×D₄	1	2	yes	—
156	C₄²×C₁₅₁	#41	1	2	yes	—
157	C₂³×C₁₅₁	—	2	1	no	—
158	C₂³×C₁₅₁	—	2	1	no	—
159	C₂³×C₁₅₁	—	2	2	no	—
160	C₂³×C₁₅₁	—	4	2	no	—
161	C₂³×C₁₅₁	C₄×D₄	1	2	yes	—
162	C₂³×C₁₅₁	C₂×#41	1	1	yes	characteristic
163	Q₈×C₁₅₁	—	2	2	no	—
164	Q₈×C₁₅₁	—	2	2	no	—
165	D₄×C₁₅₁	—	2	2	no	—
166	D₄×C₁₅₁	—	2	2	no	—
167	D₄×C₁₅₁	—	4	2	no	—
168	D₄×C₁₅₁	—	4	2	no	—
169	D₄×C₁₅₁	—	8	4	no	—
170	C₂×C₄×C₁₅₁	—	2	1	no	—
171	C₂×C₄×C₁₅₁	—	2	1	no	—
172	C₂×C₄×C₁₅₁	—	2	2	no	—
173	C₂×C₄×C₁₅₁	—	2	2	no	—
174	C₂×C₄×C₁₅₁	—	2	2	no	—
175	C₂×C₄×C₁₅₁	—	2	2	no	—
176	C₂×C₄×C₁₅₁	—	2	2	no	—
177	C₂×C₄×C₁₅₁	—	2	4	no	—
178	C₂×C₄×C₁₅₁	—	2	2	no	—
179	C₂×C₄×C₁₅₁	—	2	2	no	—
180	C₂×C₄×C₁₅₁	—	4	2	no	—
181	C₂×C₄×C₁₅₁	—	4	2	no	—
182	C₂×C₄×C₁₅₁	—	4	2	no	—
183	C₂×C₄×C₁₅₁	—	4	2	no	—
184	C₂×C₄×C₁₅₁	C₄×D₄	1	2	yes	—
185	C₂×C₄×C₁₅₁	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
191	C₈×C₁₅₁	—	2	2	no	—
192	C₈×C₁₅₁	—	2	2	no	—
193	C₈×C₁₅₁	—	4	2	no	—
194	C₈×C₁₅₁	—	4	2	no	—
195	C₈×C₁₅₁	C₄×D₄	1	2	yes	—
196	C₈×C₁₅₁	C₄×D₄	1	2	yes	—
197	C₈×C₁₅₁	#121	1	2	yes	—
198	C₈×C₁₅₁	#121	1	2	yes	—
199	C₂²×C₁₅₁	—	2	2	no	—
200	C₂²×C₁₅₁	—	2	2	no	—
201	C₂²×C₁₅₁	—	2	2	no	—
202	C₂²×C₁₅₁	—	2	2	no	—
203	C₂²×C₁₅₁	—	4	2	no	—
204	C₂²×C₁₅₁	—	4	2	no	—
205	C₂²×C₁₅₁	—	4	4	no	—
206	C₂²×C₁₅₁	—	4	2	no	—
207	C₂²×C₁₅₁	C₂×C₄×D₄	1	1	yes	characteristic
208	C₂²×C₁₅₁	#525	1	1	yes	characteristic
209	C₂²×C₁₅₁	#529	1	1	yes	characteristic
210	C₄×C₁₅₁	—	2	2	no	—
211	C₄×C₁₅₁	—	4	2	no	—
212	C₄×C₁₅₁	—	4	2	no	—
213	C₄×C₁₅₁	—	4	4	no	—
214	C₄×C₁₅₁	—	4	2	no	—
215	C₄×C₁₅₁	C₂×C₄×D₄	1	1	yes	characteristic
216	C₄×C₁₅₁	C₄×#41	1	1	yes	characteristic
217	C₄×C₁₅₁	C₂×#121	1	1	yes	characteristic
218	C₄×C₁₅₁	#532	1	1	yes	characteristic
219	C₂×C₁₅₁	—	2	1	no	—
220	C₂×C₁₅₁	—	2	1	no	—
221	C₂×C₁₅₁	—	4	2	no	—
222	C₂×C₁₅₁	—	8	2	no	—
223	C₂×C₁₅₁	C₄×#121	1	1	yes	characteristic
224	C₂×C₁₅₁	#2957	1	2	yes	—
225	#21545	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₁₅₁	#21545	1	1	yes	characteristic, direct product factor, Sylow
227	#3050	C₂×C₁₅₁	1	1	yes	characteristic
228	C₂×#443	C₂×C₁₅₁	1	1	yes	characteristic, complemented
229	#2930	C₂×C₁₅₁	1	2	yes	complemented
230	C₂×#405	C₂×C₁₅₁	1	1	yes	characteristic, complemented
231	#1974	C₂×C₁₅₁	1	1	yes	characteristic, complemented
232	#1945	C₂×C₁₅₁	1	1	yes	characteristic, complemented
233	#1938	C₂×C₁₅₁	1	2	yes	complemented
234	#1897	C₂×C₁₅₁	1	2	yes	complemented
235	#1810	C₂×C₁₅₁	1	1	yes	characteristic, complemented
236	#1772	C₂×C₁₅₁	1	1	yes	characteristic, complemented
237	#1765	C₂×C₁₅₁	1	2	yes	complemented
238	C₂×#135	C₂²×C₁₅₁	1	1	yes	characteristic
239	C₂×#131	C₂²×C₁₅₁	1	2	yes	—
240	C₂²×M₁₆	C₂²×C₁₅₁	1	1	yes	characteristic
241	C₂³×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
242	#525	C₂²×C₁₅₁	1	2	yes	—
243	C₂×#117	C₂²×C₁₅₁	1	1	yes	characteristic
244	#467	C₄×C₁₅₁	1	2	yes	complemented
245	#466	C₄×C₁₅₁	1	2	yes	complemented
246	#465	C₄×C₁₅₁	1	4	yes	complemented
247	#443	—	2	4	no	—
248	#436	—	2	4	no	—
249	#435	—	2	4	no	—
250	C₂×#108	C₂²×C₁₅₁	1	1	yes	characteristic
251	C₂×#108	C₂²×C₁₅₁	1	1	yes	characteristic
252	#427	C₂²×C₁₅₁	1	1	yes	characteristic
253	#424	C₂²×C₁₅₁	1	2	yes	—
254	C₂×#104	C₂²×C₁₅₁	1	2	yes	—
255	C₂×#104	C₂²×C₁₅₁	1	2	yes	—
256	#416	C₂²×C₁₅₁	1	2	yes	—
257	#408	C₂²×C₁₅₁	1	2	yes	—
258	#407	C₂²×C₁₅₁	1	2	yes	—
259	#405	—	2	4	no	—
260	#405	C₂²×C₁₅₁	1	2	yes	—
261	C₂×#97	C₂²×C₁₅₁	1	1	yes	characteristic
262	C₂×#97	C₂²×C₁₅₁	1	1	yes	characteristic
263	C₂×C₄×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
265	#341	C₂²×C₁₅₁	1	2	yes	—
266	#339	C₂²×C₁₅₁	1	2	yes	—
267	#339	C₂²×C₁₅₁	1	2	yes	—
268	C₂×#41	C₂³×C₁₅₁	1	2	yes	—
269	C₂³×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
270	#135	—	2	2	no	—
271	#135	—	2	2	no	—
272	C₂×Q₁₆	C₂×C₄×C₁₅₁	1	1	yes	characteristic
273	C₂×SD₁₆	C₂×C₄×C₁₅₁	1	2	yes	—
274	C₂×D₈	C₂×C₄×C₁₅₁	1	1	yes	characteristic
275	#131	—	2	4	no	—
276	#131	—	2	4	no	—
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	D₄×C₁₅₁	1	2	yes	—
281	C₂×M₁₆	D₄×C₁₅₁	1	2	yes	—
282	C₂×M₁₆	C₂³×C₁₅₁	1	2	yes	—
283	C₂×M₁₆	C₂³×C₁₅₁	1	2	yes	—
284	C₂²×C₈	—	2	2	no	—
285	C₂²×C₈	—	2	2	no	—
286	C₂²×C₈	—	2	2	no	—
287	C₂²×C₈	C₂×C₄×C₁₅₁	1	2	yes	—
288	C₂²×C₈	C₂×C₄×C₁₅₁	1	2	yes	—
289	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
293	#123	—	2	2	no	—
294	C₂²⋊Q₈	C₂×C₄×C₁₅₁	1	4	yes	—
295	#121	C₂×C₄×C₁₅₁	1	4	yes	—
296	#120	—	2	2	no	—
297	C₄×D₄	—	2	4	no	—
298	#117	—	2	2	no	—
299	#117	—	2	2	no	—
300	#117	C₂³×C₁₅₁	1	2	yes	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
305	#108	—	2	2	no	—
306	#108	—	2	2	no	—
307	#107	C₂×C₄×C₁₅₁	1	2	yes	—
308	#106	C₂×C₄×C₁₅₁	1	2	yes	—
309	C₄⋊C₈	—	2	4	no	—
310	#104	—	2	4	no	—
311	#104	—	2	4	no	—
312	#103	C₂×C₄×C₁₅₁	1	4	yes	—
313	#102	C₂×C₄×C₁₅₁	1	4	yes	—
314	C₂²⋊C₈	—	2	4	no	—
315	C₂²⋊C₈	—	2	4	no	—
316	#97	—	2	2	no	—
317	#97	—	2	2	no	—
318	#97	—	2	2	no	—
319	C₄×C₈	—	2	2	no	—
320	C₄×C₈	—	2	2	no	—
321	C₄×C₈	D₄×C₁₅₁	1	4	yes	complemented
322	C₂⁴	#41×C₁₅₁	1	1	yes	characteristic
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	#41	—	2	2	no	—
327	C₂×Q₈	C₂²×C₄×C₁₅₁	1	2	yes	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	C₂²×C₄×C₁₅₁	1	2	yes	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	C₂²×C₄×C₁₅₁	1	2	yes	—
339	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
340	C₂²×C₄	#41×C₁₅₁	1	1	yes	characteristic
341	C₂²×C₄	C₂⁴×C₁₅₁	1	1	yes	characteristic
342	Q₁₆	—	2	2	no	—
343	SD₁₆	—	2	4	no	—
344	D₈	—	2	2	no	—
345	M₁₆	—	2	4	no	—
346	M₁₆	—	2	4	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	—	2	2	no	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	4	4	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	—	2	4	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	4	4	no	—
361	C₂×C₈	C₂²×C₄×C₁₅₁	1	2	yes	—
362	C₂×C₈	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
363	C₂×C₈	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
364	C₂×C₈	C₂×D₄×C₁₅₁	1	2	yes	—
365	C₂×C₈	C₂×D₄×C₁₅₁	1	2	yes	—
366	C₂×C₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
367	C₂×C₈	C₂×D₄×C₁₅₁	1	2	yes	—
368	C₂×C₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
369	C₂×C₈	#41×C₁₅₁	1	2	yes	—
370	C₂×C₈	#41×C₁₅₁	1	2	yes	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	C₂²×C₄×C₁₅₁	1	4	yes	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	1	no	—
381	C₄²	C₂×D₄×C₁₅₁	1	2	yes	—
382	C₄²	#41×C₁₅₁	1	2	yes	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	C₄×D₄×C₁₅₁	1	2	yes	—
388	C₂³	C₂×#41×C₁₅₁	1	1	yes	characteristic
389	Q₈	—	2	2	no	—
390	Q₈	—	2	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	2	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	8	4	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	C₄×D₄×C₁₅₁	1	2	yes	—
411	C₂×C₄	C₂³×C₄×C₁₅₁	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
414	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
415	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
416	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
417	C₈	—	2	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	4	2	no	—
420	C₈	—	4	2	no	—
421	C₈	C₄×D₄×C₁₅₁	1	2	yes	—
422	C₈	C₄×D₄×C₁₅₁	1	2	yes	—
423	C₈	#121×C₁₅₁	1	2	yes	—
424	C₈	#121×C₁₅₁	1	2	yes	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	2	no	—
433	C₂²	C₂×C₄×D₄×C₁₅₁	1	1	yes	characteristic
434	C₂²	#525×C₁₅₁	1	1	yes	characteristic
435	C₂²	#529×C₁₅₁	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	4	no	—
440	C₄	—	4	2	no	—
441	C₄	C₂×C₄×D₄×C₁₅₁	1	1	yes	characteristic
442	C₄	C₄×#41×C₁₅₁	1	1	yes	characteristic
443	C₄	C₂×#121×C₁₅₁	1	1	yes	characteristic
444	C₄	#532×C₁₅₁	1	1	yes	characteristic
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	4	2	no	—
448	C₂	—	8	2	no	—
449	C₂	C₄×#121×C₁₅₁	1	1	yes	characteristic
450	C₂	#2957×C₁₅₁	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₅₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₅₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₅₁
socle	C₂²×C₁₅₁	C₂×C₄×D₄
prime radical	#3050×C₁₅₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₅₁ ◁ C₂²×M₁₆×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#443×C₁₅₁	C₂	semidirect
3. #2930×C₁₅₁	C₂	semidirect
4. C₂×#405×C₁₅₁	C₂	semidirect
5. #1974×C₁₅₁	C₂	semidirect
6. #1945×C₁₅₁	C₂	semidirect
7. #1938×C₁₅₁	C₂	semidirect
8. #1897×C₁₅₁	C₂	semidirect
9. #1810×C₁₅₁	C₂	semidirect
10. #1772×C₁₅₁	C₂	semidirect
11. #1765×C₁₅₁	C₂	semidirect
18. #467×C₁₅₁	C₄	semidirect
19. #466×C₁₅₁	C₄	semidirect
20. #465×C₁₅₁	C₄	semidirect
95. C₄×C₈×C₁₅₁	D₄	semidirect
225. #21545	C₁₅₁	direct (N × H)
226. C₁₅₁	#21545	direct (N × H)
228. C₂×#443	C₂×C₁₅₁	semidirect
229. #2930	C₂×C₁₅₁	semidirect
230. C₂×#405	C₂×C₁₅₁	semidirect
231. #1974	C₂×C₁₅₁	semidirect
232. #1945	C₂×C₁₅₁	semidirect
233. #1938	C₂×C₁₅₁	semidirect
234. #1897	C₂×C₁₅₁	semidirect
235. #1810	C₂×C₁₅₁	semidirect
236. #1772	C₂×C₁₅₁	semidirect
237. #1765	C₂×C₁₅₁	semidirect
244. #467	C₄×C₁₅₁	semidirect
245. #466	C₄×C₁₅₁	semidirect
246. #465	C₄×C₁₅₁	semidirect
321. C₄×C₈	D₄×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
#3050×C₁₅₁	2
C₂×#443×C₁₅₁	2
#2930×C₁₅₁	2
C₂×#405×C₁₅₁	2
#1974×C₁₅₁	2
#1945×C₁₅₁	2
#1938×C₁₅₁	2
#1897×C₁₅₁	2
#1810×C₁₅₁	2
#1772×C₁₅₁	2
#1765×C₁₅₁	2
#21545	151

Subgroups — C151×#21545 #50326470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#21545 #50326470