Subgroups — C₁₅₁×#24279 #50329204

Order 38656.

1328 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#471×C₁₅₁	C₂	1	2	yes	maximal, complemented
3	#3005×C₁₅₁	C₂	1	2	yes	maximal, complemented
4	#2929×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2047×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#2045×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#2020×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#2018×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1977×C₁₅₁	C₂	1	2	yes	maximal, complemented
10	#1810×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1785×C₁₅₁	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₁₅₁	C₂²	1	2	yes	—
13	C₂×#137×C₁₅₁	C₂²	1	2	yes	—
14	C₂×AGL(1,ℤ/8)×C₁₅₁	C₂²	1	2	yes	—
15	C₂×#135×C₁₅₁	—	2	8	no	—
16	C₂×#135×C₁₅₁	—	2	2	no	—
17	C₂×#135×C₁₅₁	—	2	2	no	—
18	C₂²×Q₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₁₅₁	C₂²	1	2	yes	—
20	C₂²×D₈×C₁₅₁	C₂²	1	1	yes	characteristic
21	C₂×#131×C₁₅₁	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
23	#525×C₁₅₁	C₂²	1	1	yes	characteristic
24	#471×C₁₅₁	—	2	8	no	—
25	#452×C₁₅₁	—	2	4	no	—
26	#449×C₁₅₁	—	2	4	no	—
27	#435×C₁₅₁	—	2	2	no	—
28	C₈×D₄×C₁₅₁	—	2	2	no	—
29	C₂×#108×C₁₅₁	C₂²	1	2	yes	—
30	#424×C₁₅₁	C₂²	1	1	yes	characteristic
31	#419×C₁₅₁	C₂²	1	2	yes	—
32	#418×C₁₅₁	C₂²	1	2	yes	—
33	C₂×#101×C₁₅₁	C₂²	1	2	yes	—
34	C₂×#101×C₁₅₁	C₂²	1	2	yes	—
35	C₂×#100×C₁₅₁	C₂²	1	2	yes	—
36	C₂×#100×C₁₅₁	C₂²	1	2	yes	—
37	#408×C₁₅₁	C₂²	1	1	yes	characteristic
38	#407×C₁₅₁	C₂²	1	1	yes	characteristic
39	#407×C₁₅₁	C₂²	1	2	yes	—
40	#405×C₁₅₁	C₂²	1	1	yes	characteristic
41	#341×C₁₅₁	C₂²	1	1	yes	characteristic
42	#341×C₁₅₁	C₂²	1	1	yes	characteristic
43	C₂×#41×C₁₅₁	—	2	4	no	—
44	C₂×#41×C₁₅₁	—	2	4	no	—
45	C₂×#41×C₁₅₁	—	2	4	no	—
46	C₂×#41×C₁₅₁	—	2	4	no	—
47	C₂×#41×C₁₅₁	—	4	2	no	—
48	C₂×#41×C₁₅₁	—	4	2	no	—
49	C₂×#41×C₁₅₁	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₁₅₁	C₂³	1	2	yes	—
51	C₂²×D₄×C₁₅₁	—	2	2	no	—
52	C₂²×D₄×C₁₅₁	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₅₁	—	2	2	no	—
54	C₂³×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
55	#137×C₁₅₁	—	2	4	no	—
56	#137×C₁₅₁	—	4	2	no	—
57	AGL(1,ℤ/8)×C₁₅₁	—	2	4	no	—
58	AGL(1,ℤ/8)×C₁₅₁	—	4	2	no	—
59	#135×C₁₅₁	—	2	16	no	—
60	#135×C₁₅₁	—	2	16	no	—
61	C₂×Q₁₆×C₁₅₁	—	2	2	no	—
62	C₂×Q₁₆×C₁₅₁	—	2	4	no	—
63	C₂×Q₁₆×C₁₅₁	—	2	2	no	—
64	C₂×SD₁₆×C₁₅₁	—	2	2	no	—
65	C₂×SD₁₆×C₁₅₁	—	2	2	no	—
66	C₂×SD₁₆×C₁₅₁	—	2	2	no	—
67	C₂×SD₁₆×C₁₅₁	—	2	4	no	—
68	C₂×SD₁₆×C₁₅₁	—	2	2	no	—
69	C₂×SD₁₆×C₁₅₁	D₄	1	8	yes	complemented
70	C₂×D₈×C₁₅₁	—	2	4	no	—
71	C₂×D₈×C₁₅₁	—	2	2	no	—
72	C₂×D₈×C₁₅₁	—	2	2	no	—
73	#131×C₁₅₁	—	2	4	no	—
74	C₂×M₁₆×C₁₅₁	—	2	1	no	—
75	C₂×M₁₆×C₁₅₁	C₂³	1	2	yes	—
76	C₂×M₁₆×C₁₅₁	C₂³	1	2	yes	—
77	C₂×M₁₆×C₁₅₁	C₂³	1	1	yes	characteristic
78	C₂×M₁₆×C₁₅₁	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₅₁	—	2	4	no	—
80	C₂²×C₈×C₁₅₁	—	2	1	no	—
81	C₂²×C₈×C₁₅₁	D₄	1	2	yes	—
82	C₂²×C₈×C₁₅₁	D₄	1	2	yes	—
83	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
85	#123×C₁₅₁	—	2	1	no	—
86	C₂²⋊Q₈×C₁₅₁	D₄	1	2	yes	—
87	#121×C₁₅₁	D₄	1	2	yes	—
88	#120×C₁₅₁	—	2	1	no	—
89	C₄×D₄×C₁₅₁	—	2	2	no	—
90	#117×C₁₅₁	C₂³	1	1	yes	characteristic
91	#108×C₁₅₁	—	2	4	no	—
92	C₄⋊C₈×C₁₅₁	—	2	2	no	—
93	#103×C₁₅₁	—	2	4	no	—
94	#102×C₁₅₁	—	2	4	no	—
95	#101×C₁₅₁	—	2	4	no	—
96	#101×C₁₅₁	—	4	2	no	—
97	#100×C₁₅₁	—	2	4	no	—
98	#100×C₁₅₁	—	4	2	no	—
99	C₂²⋊C₈×C₁₅₁	—	2	2	no	—
100	C₂²⋊C₈×C₁₅₁	—	2	4	no	—
101	C₂²⋊C₈×C₁₅₁	—	2	2	no	—
102	#97×C₁₅₁	—	2	1	no	—
103	C₄×C₈×C₁₅₁	—	2	1	no	—
104	C₂⁴×C₁₅₁	—	2	2	no	—
105	C₂⁴×C₁₅₁	#41	1	1	yes	characteristic
106	#41×C₁₅₁	—	2	16	no	—
107	#41×C₁₅₁	—	2	2	no	—
108	#41×C₁₅₁	—	2	2	no	—
109	#41×C₁₅₁	—	4	8	no	—
110	#41×C₁₅₁	—	4	8	no	—
111	#41×C₁₅₁	—	4	8	no	—
112	C₂×Q₈×C₁₅₁	—	2	2	no	—
113	C₂×Q₈×C₁₅₁	—	2	2	no	—
114	C₂×Q₈×C₁₅₁	—	2	2	no	—
115	C₂×Q₈×C₁₅₁	—	2	2	no	—
116	C₂×Q₈×C₁₅₁	—	2	2	no	—
117	C₂×Q₈×C₁₅₁	C₂×D₄	1	4	yes	—
118	C₂×Q₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
119	C₂×D₄×C₁₅₁	—	2	2	no	—
120	C₂×D₄×C₁₅₁	—	2	1	no	—
121	C₂×D₄×C₁₅₁	—	2	2	no	—
122	C₂×D₄×C₁₅₁	—	2	2	no	—
123	C₂×D₄×C₁₅₁	—	2	2	no	—
124	C₂×D₄×C₁₅₁	—	2	2	no	—
125	C₂×D₄×C₁₅₁	—	2	2	no	—
126	C₂×D₄×C₁₅₁	—	4	4	no	—
127	C₂×D₄×C₁₅₁	—	4	4	no	—
128	C₂×D₄×C₁₅₁	—	4	4	no	—
129	C₂×D₄×C₁₅₁	C₂×D₄	1	4	yes	—
130	C₂×D₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₅₁	—	2	2	no	—
132	C₂²×C₄×C₁₅₁	—	2	2	no	—
133	C₂²×C₄×C₁₅₁	—	2	2	no	—
134	C₂²×C₄×C₁₅₁	—	2	1	no	—
135	C₂²×C₄×C₁₅₁	—	4	4	no	—
136	C₂²×C₄×C₁₅₁	—	4	4	no	—
137	C₂²×C₄×C₁₅₁	—	4	4	no	—
138	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₅₁	#41	1	1	yes	characteristic
141	C₂²×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
142	Q₁₆×C₁₅₁	—	2	8	no	—
143	Q₁₆×C₁₅₁	—	4	4	no	—
144	SD₁₆×C₁₅₁	—	2	8	no	—
145	SD₁₆×C₁₅₁	—	2	8	no	—
146	SD₁₆×C₁₅₁	—	4	4	no	—
147	SD₁₆×C₁₅₁	—	4	4	no	—
148	D₈×C₁₅₁	—	2	8	no	—
149	D₈×C₁₅₁	—	4	4	no	—
150	M₁₆×C₁₅₁	—	2	2	no	—
151	M₁₆×C₁₅₁	—	2	2	no	—
152	M₁₆×C₁₅₁	—	2	2	no	—
153	M₁₆×C₁₅₁	—	2	2	no	—
154	M₁₆×C₁₅₁	—	2	2	no	—
155	M₁₆×C₁₅₁	—	2	2	no	—
156	M₁₆×C₁₅₁	—	4	2	no	—
157	C₂×C₈×C₁₅₁	—	2	2	no	—
158	C₂×C₈×C₁₅₁	—	2	4	no	—
159	C₂×C₈×C₁₅₁	—	2	4	no	—
160	C₂×C₈×C₁₅₁	—	2	1	no	—
161	C₂×C₈×C₁₅₁	—	2	2	no	—
162	C₂×C₈×C₁₅₁	—	2	2	no	—
163	C₂×C₈×C₁₅₁	—	2	1	no	—
164	C₂×C₈×C₁₅₁	—	4	2	no	—
165	C₂×C₈×C₁₅₁	C₂×D₄	1	2	yes	—
166	C₂×C₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
167	C₂×C₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
168	C₂×C₈×C₁₅₁	C₂×D₄	1	4	yes	—
169	C₄⋊C₄×C₁₅₁	—	2	2	no	—
170	C₄⋊C₄×C₁₅₁	C₂×D₄	1	2	yes	—
171	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
172	C₂²⋊C₄×C₁₅₁	—	2	1	no	—
173	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
174	C₄²×C₁₅₁	—	2	1	no	—
175	C₂³×C₁₅₁	—	2	2	no	—
176	C₂³×C₁₅₁	—	2	1	no	—
177	C₂³×C₁₅₁	—	2	4	no	—
178	C₂³×C₁₅₁	—	4	2	no	—
179	C₂³×C₁₅₁	—	4	2	no	—
180	C₂³×C₁₅₁	—	4	2	no	—
181	C₂³×C₁₅₁	—	8	4	no	—
182	C₂³×C₁₅₁	#121	1	2	yes	—
183	C₂³×C₁₅₁	C₂×#41	1	1	yes	characteristic
184	Q₈×C₁₅₁	—	2	4	no	—
185	Q₈×C₁₅₁	—	2	4	no	—
186	Q₈×C₁₅₁	—	2	2	no	—
187	Q₈×C₁₅₁	—	4	2	no	—
188	Q₈×C₁₅₁	—	4	2	no	—
189	D₄×C₁₅₁	—	2	4	no	—
190	D₄×C₁₅₁	—	2	2	no	—
191	D₄×C₁₅₁	—	2	4	no	—
192	D₄×C₁₅₁	—	4	16	no	—
193	D₄×C₁₅₁	—	4	4	no	—
194	D₄×C₁₅₁	—	4	2	no	—
195	D₄×C₁₅₁	—	4	2	no	—
196	D₄×C₁₅₁	—	4	2	no	—
197	C₂×C₄×C₁₅₁	—	2	2	no	—
198	C₂×C₄×C₁₅₁	—	2	2	no	—
199	C₂×C₄×C₁₅₁	—	2	2	no	—
200	C₂×C₄×C₁₅₁	—	2	4	no	—
201	C₂×C₄×C₁₅₁	—	2	1	no	—
202	C₂×C₄×C₁₅₁	—	2	2	no	—
203	C₂×C₄×C₁₅₁	—	2	4	no	—
204	C₂×C₄×C₁₅₁	—	4	16	no	—
205	C₂×C₄×C₁₅₁	—	4	2	no	—
206	C₂×C₄×C₁₅₁	—	4	2	no	—
207	C₂×C₄×C₁₅₁	—	4	1	no	—
208	C₂×C₄×C₁₅₁	—	4	1	no	—
209	C₂×C₄×C₁₅₁	#121	1	2	yes	—
210	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₅₁	C₂²×D₄	1	2	yes	—
212	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₅₁	H(5,𝔽₂)	1	2	yes	—
214	C₈×C₁₅₁	—	2	2	no	—
215	C₈×C₁₅₁	—	4	1	no	—
216	C₈×C₁₅₁	—	4	1	no	—
217	C₈×C₁₅₁	—	4	2	no	—
218	C₈×C₁₅₁	—	4	2	no	—
219	C₈×C₁₅₁	#120	1	2	yes	—
220	C₈×C₁₅₁	#120	1	2	yes	—
221	C₂²×C₁₅₁	—	2	2	no	—
222	C₂²×C₁₅₁	—	2	2	no	—
223	C₂²×C₁₅₁	—	2	2	no	—
224	C₂²×C₁₅₁	—	2	2	no	—
225	C₂²×C₁₅₁	—	4	4	no	—
226	C₂²×C₁₅₁	—	4	4	no	—
227	C₂²×C₁₅₁	—	4	1	no	—
228	C₂²×C₁₅₁	—	4	2	no	—
229	C₂²×C₁₅₁	—	8	4	no	—
230	C₂²×C₁₅₁	—	8	4	no	—
231	C₂²×C₁₅₁	—	8	4	no	—
232	C₂²×C₁₅₁	C₂×#121	1	1	yes	characteristic
233	C₂²×C₁₅₁	#546	1	2	yes	—
234	C₄×C₁₅₁	—	2	2	no	—
235	C₄×C₁₅₁	—	4	4	no	—
236	C₄×C₁₅₁	—	4	1	no	—
237	C₄×C₁₅₁	—	4	2	no	—
238	C₄×C₁₅₁	C₂×#120	1	1	yes	characteristic
239	C₄×C₁₅₁	#535	1	1	yes	characteristic
240	C₄×C₁₅₁	D₄²	1	2	yes	—
241	C₂×C₁₅₁	—	2	2	no	—
242	C₂×C₁₅₁	—	4	2	no	—
243	C₂×C₁₅₁	—	8	1	no	—
244	C₂×C₁₅₁	—	8	4	no	—
245	C₂×C₁₅₁	#2408	1	1	yes	characteristic
246	C₂×C₁₅₁	#3067	1	2	yes	—
247	#24279	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₁₅₁	#24279	1	1	yes	characteristic, direct product factor, Sylow
249	C₂²×#135	C₂×C₁₅₁	1	1	yes	characteristic, complemented
250	C₂×#471	C₂×C₁₅₁	1	2	yes	complemented
251	#3005	C₂×C₁₅₁	1	2	yes	complemented
252	#2929	C₂×C₁₅₁	1	1	yes	characteristic, complemented
253	#2047	C₂×C₁₅₁	1	1	yes	characteristic, complemented
254	#2045	C₂×C₁₅₁	1	1	yes	characteristic, complemented
255	#2020	C₂×C₁₅₁	1	1	yes	characteristic, complemented
256	#2018	C₂×C₁₅₁	1	1	yes	characteristic, complemented
257	#1977	C₂×C₁₅₁	1	2	yes	complemented
258	#1810	C₂×C₁₅₁	1	1	yes	characteristic, complemented
259	#1785	C₂×C₁₅₁	1	2	yes	complemented
260	C₂²×#41	C₂²×C₁₅₁	1	2	yes	—
261	C₂×#137	C₂²×C₁₅₁	1	2	yes	—
262	C₂×AGL(1,ℤ/8)	C₂²×C₁₅₁	1	2	yes	—
263	C₂×#135	—	2	8	no	—
264	C₂×#135	—	2	2	no	—
265	C₂×#135	—	2	2	no	—
266	C₂²×Q₁₆	C₂²×C₁₅₁	1	1	yes	characteristic
267	C₂²×SD₁₆	C₂²×C₁₅₁	1	2	yes	—
268	C₂²×D₈	C₂²×C₁₅₁	1	1	yes	characteristic
269	C₂×#131	C₂²×C₁₅₁	1	1	yes	characteristic
270	C₂³×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
271	#525	C₂²×C₁₅₁	1	1	yes	characteristic
272	#471	—	2	8	no	—
273	#452	—	2	4	no	—
274	#449	—	2	4	no	—
275	#435	—	2	2	no	—
276	C₈×D₄	—	2	2	no	—
277	C₂×#108	C₂²×C₁₅₁	1	2	yes	—
278	#424	C₂²×C₁₅₁	1	1	yes	characteristic
279	#419	C₂²×C₁₅₁	1	2	yes	—
280	#418	C₂²×C₁₅₁	1	2	yes	—
281	C₂×#101	C₂²×C₁₅₁	1	2	yes	—
282	C₂×#101	C₂²×C₁₅₁	1	2	yes	—
283	C₂×#100	C₂²×C₁₅₁	1	2	yes	—
284	C₂×#100	C₂²×C₁₅₁	1	2	yes	—
285	#408	C₂²×C₁₅₁	1	1	yes	characteristic
286	#407	C₂²×C₁₅₁	1	2	yes	—
287	#407	C₂²×C₁₅₁	1	1	yes	characteristic
288	#405	C₂²×C₁₅₁	1	1	yes	characteristic
289	#341	C₂²×C₁₅₁	1	1	yes	characteristic
290	#341	C₂²×C₁₅₁	1	1	yes	characteristic
291	C₂×#41	—	2	4	no	—
292	C₂×#41	—	2	4	no	—
293	C₂×#41	—	2	4	no	—
294	C₂×#41	—	2	4	no	—
295	C₂×#41	—	4	2	no	—
296	C₂×#41	—	4	2	no	—
297	C₂×#41	C₂³×C₁₅₁	1	1	yes	characteristic
298	C₂²×Q₈	C₂³×C₁₅₁	1	2	yes	—
299	C₂²×D₄	—	2	2	no	—
300	C₂²×D₄	C₂³×C₁₅₁	1	2	yes	—
301	C₂³×C₄	—	2	2	no	—
302	C₂³×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
303	#137	—	2	4	no	—
304	#137	—	4	2	no	—
305	AGL(1,ℤ/8)	—	2	4	no	—
306	AGL(1,ℤ/8)	—	4	2	no	—
307	#135	—	2	16	no	—
308	#135	—	2	16	no	—
309	C₂×Q₁₆	—	2	4	no	—
310	C₂×Q₁₆	—	2	2	no	—
311	C₂×Q₁₆	—	2	2	no	—
312	C₂×SD₁₆	—	2	2	no	—
313	C₂×SD₁₆	—	2	2	no	—
314	C₂×SD₁₆	—	2	2	no	—
315	C₂×SD₁₆	—	2	2	no	—
316	C₂×SD₁₆	—	2	4	no	—
317	C₂×SD₁₆	D₄×C₁₅₁	1	8	yes	complemented
318	C₂×D₈	—	2	4	no	—
319	C₂×D₈	—	2	2	no	—
320	C₂×D₈	—	2	2	no	—
321	#131	—	2	4	no	—
322	C₂×M₁₆	—	2	1	no	—
323	C₂×M₁₆	C₂³×C₁₅₁	1	1	yes	characteristic
324	C₂×M₁₆	C₂³×C₁₅₁	1	2	yes	—
325	C₂×M₁₆	C₂³×C₁₅₁	1	2	yes	—
326	C₂×M₁₆	C₂³×C₁₅₁	1	1	yes	characteristic
327	C₂²×C₈	—	2	4	no	—
328	C₂²×C₈	—	2	1	no	—
329	C₂²×C₈	D₄×C₁₅₁	1	2	yes	—
330	C₂²×C₈	D₄×C₁₅₁	1	2	yes	—
331	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
332	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
333	#123	—	2	1	no	—
334	C₂²⋊Q₈	D₄×C₁₅₁	1	2	yes	—
335	#121	D₄×C₁₅₁	1	2	yes	—
336	#120	—	2	1	no	—
337	C₄×D₄	—	2	2	no	—
338	#117	C₂³×C₁₅₁	1	1	yes	characteristic
339	#108	—	2	4	no	—
340	C₄⋊C₈	—	2	2	no	—
341	#103	—	2	4	no	—
342	#102	—	2	4	no	—
343	#101	—	2	4	no	—
344	#101	—	4	2	no	—
345	#100	—	2	4	no	—
346	#100	—	4	2	no	—
347	C₂²⋊C₈	—	2	2	no	—
348	C₂²⋊C₈	—	2	4	no	—
349	C₂²⋊C₈	—	2	2	no	—
350	#97	—	2	1	no	—
351	C₄×C₈	—	2	1	no	—
352	C₂⁴	—	2	2	no	—
353	C₂⁴	#41×C₁₅₁	1	1	yes	characteristic
354	#41	—	2	16	no	—
355	#41	—	2	2	no	—
356	#41	—	2	2	no	—
357	#41	—	4	8	no	—
358	#41	—	4	8	no	—
359	#41	—	4	8	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	C₂×D₄×C₁₅₁	1	4	yes	—
366	C₂×Q₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	4	4	no	—
375	C₂×D₄	—	4	4	no	—
376	C₂×D₄	—	4	4	no	—
377	C₂×D₄	C₂×D₄×C₁₅₁	1	4	yes	—
378	C₂×D₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	4	4	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	—	4	4	no	—
386	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
388	C₂²×C₄	#41×C₁₅₁	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴×C₁₅₁	1	1	yes	characteristic
390	Q₁₆	—	2	8	no	—
391	Q₁₆	—	4	4	no	—
392	SD₁₆	—	2	8	no	—
393	SD₁₆	—	2	8	no	—
394	SD₁₆	—	4	4	no	—
395	SD₁₆	—	4	4	no	—
396	D₈	—	2	8	no	—
397	D₈	—	4	4	no	—
398	M₁₆	—	2	2	no	—
399	M₁₆	—	2	2	no	—
400	M₁₆	—	2	2	no	—
401	M₁₆	—	2	2	no	—
402	M₁₆	—	2	2	no	—
403	M₁₆	—	2	2	no	—
404	M₁₆	—	4	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	4	no	—
407	C₂×C₈	—	2	4	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	4	2	no	—
413	C₂×C₈	C₂×D₄×C₁₅₁	1	2	yes	—
414	C₂×C₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
415	C₂×C₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
416	C₂×C₈	C₂×D₄×C₁₅₁	1	4	yes	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	C₂×D₄×C₁₅₁	1	2	yes	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₄²	—	2	1	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	1	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	8	4	no	—
430	C₂³	#121×C₁₅₁	1	2	yes	—
431	C₂³	C₂×#41×C₁₅₁	1	1	yes	characteristic
432	Q₈	—	2	4	no	—
433	Q₈	—	2	2	no	—
434	Q₈	—	2	4	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	4	2	no	—
437	D₄	—	2	4	no	—
438	D₄	—	2	2	no	—
439	D₄	—	2	4	no	—
440	D₄	—	4	4	no	—
441	D₄	—	4	16	no	—
442	D₄	—	4	2	no	—
443	D₄	—	4	2	no	—
444	D₄	—	4	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	4	16	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	#121×C₁₅₁	1	2	yes	—
458	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₄×C₁₅₁	1	2	yes	—
460	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
461	C₂×C₄	H(5,𝔽₂)×C₁₅₁	1	2	yes	—
462	C₈	—	2	2	no	—
463	C₈	—	4	1	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	2	no	—
466	C₈	—	4	2	no	—
467	C₈	#120×C₁₅₁	1	2	yes	—
468	C₈	#120×C₁₅₁	1	2	yes	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	8	4	no	—
478	C₂²	—	8	4	no	—
479	C₂²	—	8	4	no	—
480	C₂²	C₂×#121×C₁₅₁	1	1	yes	characteristic
481	C₂²	#546×C₁₅₁	1	2	yes	—
482	C₄	—	2	2	no	—
483	C₄	—	4	4	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	2	no	—
486	C₄	C₂×#120×C₁₅₁	1	1	yes	characteristic
487	C₄	#535×C₁₅₁	1	1	yes	characteristic
488	C₄	D₄²×C₁₅₁	1	2	yes	—
489	C₂	—	2	2	no	—
490	C₂	—	4	2	no	—
491	C₂	—	8	1	no	—
492	C₂	—	8	4	no	—
493	C₂	#2408×C₁₅₁	1	1	yes	characteristic
494	C₂	#3067×C₁₅₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₅₁	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₅₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₅₁ ◁ C₂³×C₄×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#135×C₁₅₁	C₂	semidirect
2. C₂×#471×C₁₅₁	C₂	semidirect
3. #3005×C₁₅₁	C₂	semidirect
4. #2929×C₁₅₁	C₂	semidirect
5. #2047×C₁₅₁	C₂	semidirect
6. #2045×C₁₅₁	C₂	semidirect
7. #2020×C₁₅₁	C₂	semidirect
8. #2018×C₁₅₁	C₂	semidirect
9. #1977×C₁₅₁	C₂	semidirect
10. #1810×C₁₅₁	C₂	semidirect
11. #1785×C₁₅₁	C₂	semidirect
69. C₂×SD₁₆×C₁₅₁	D₄	semidirect
247. #24279	C₁₅₁	direct (N × H)
248. C₁₅₁	#24279	direct (N × H)
249. C₂²×#135	C₂×C₁₅₁	semidirect
250. C₂×#471	C₂×C₁₅₁	semidirect
251. #3005	C₂×C₁₅₁	semidirect
252. #2929	C₂×C₁₅₁	semidirect
253. #2047	C₂×C₁₅₁	semidirect
254. #2045	C₂×C₁₅₁	semidirect
255. #2020	C₂×C₁₅₁	semidirect
256. #2018	C₂×C₁₅₁	semidirect
257. #1977	C₂×C₁₅₁	semidirect
258. #1810	C₂×C₁₅₁	semidirect
259. #1785	C₂×C₁₅₁	semidirect
317. C₂×SD₁₆	D₄×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#135×C₁₅₁	2
C₂×#471×C₁₅₁	2
#3005×C₁₅₁	2
#2929×C₁₅₁	2
#2047×C₁₅₁	2
#2045×C₁₅₁	2
#2020×C₁₅₁	2
#2018×C₁₅₁	2
#1977×C₁₅₁	2
#1810×C₁₅₁	2
#1785×C₁₅₁	2
#24279	151

Subgroups — C151×#24279 #50329204

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#24279 #50329204