Subgroups — C₁₅₁×#23015 #50327940

Order 38656.

892 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3035×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#443×C₁₅₁	C₂	1	2	yes	maximal, complemented
3	#2935×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2906×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#1962×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#1950×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1937×C₁₅₁	C₂	1	2	yes	maximal, complemented
8	#1876×C₁₅₁	C₂	1	2	yes	maximal, complemented
9	#1866×C₁₅₁	C₂	1	2	yes	maximal, complemented
10	C₄×C₄⋊C₈×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#104×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₁₅₁	C₂²	1	2	yes	—
13	C₂×#131×C₁₅₁	C₂²	1	2	yes	—
14	C₂×#131×C₁₅₁	C₂²	1	2	yes	—
15	#532×C₁₅₁	C₂²	1	1	yes	characteristic
16	C₄×#41×C₁₅₁	C₂²	1	1	yes	characteristic
17	#464×C₁₅₁	C₄	1	2	yes	complemented
18	#463×C₁₅₁	C₄	1	2	yes	complemented
19	#462×C₁₅₁	C₄	1	1	yes	characteristic, complemented
20	#461×C₁₅₁	C₄	1	1	yes	characteristic, complemented
21	#460×C₁₅₁	C₄	1	1	yes	characteristic, complemented
22	#459×C₁₅₁	C₄	1	1	yes	characteristic, complemented
23	#443×C₁₅₁	—	2	8	no	—
24	#436×C₁₅₁	—	2	1	no	—
25	#435×C₁₅₁	—	2	2	no	—
26	C₈×D₄×C₁₅₁	—	2	1	no	—
27	C₂×#108×C₁₅₁	C₂²	1	2	yes	—
28	#424×C₁₅₁	—	2	2	no	—
29	#424×C₁₅₁	C₂²	1	2	yes	—
30	#423×C₁₅₁	—	2	1	no	—
31	#423×C₁₅₁	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₁₅₁	—	2	1	no	—
33	C₂×C₄⋊C₈×C₁₅₁	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₁₅₁	C₂²	1	1	yes	characteristic
35	C₂×#104×C₁₅₁	C₂²	1	1	yes	characteristic
36	C₂×#104×C₁₅₁	C₂²	1	2	yes	—
37	C₂×#104×C₁₅₁	C₂²	1	2	yes	—
38	C₂×#104×C₁₅₁	C₂²	1	1	yes	characteristic
39	#416×C₁₅₁	C₂²	1	2	yes	—
40	#408×C₁₅₁	C₂²	1	2	yes	—
41	C₄×M₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₁₅₁	C₂²	1	2	yes	—
43	C₄³×C₁₅₁	C₂²	1	1	yes	characteristic
44	#341×C₁₅₁	C₂²	1	2	yes	—
45	#339×C₁₅₁	C₂²	1	1	yes	characteristic
46	#339×C₁₅₁	C₂²	1	1	yes	characteristic
47	#336×C₁₅₁	C₂²	1	2	yes	—
48	C₂×#41×C₁₅₁	C₂³	1	2	yes	—
49	C₂×#41×C₁₅₁	C₂³	1	1	yes	characteristic
50	#135×C₁₅₁	—	2	4	no	—
51	#135×C₁₅₁	—	2	4	no	—
52	C₂×Q₁₆×C₁₅₁	C₂×C₄	1	2	yes	—
53	C₂×SD₁₆×C₁₅₁	C₂×C₄	1	2	yes	—
54	C₂×SD₁₆×C₁₅₁	C₂×C₄	1	2	yes	—
55	C₂×D₈×C₁₅₁	C₂×C₄	1	2	yes	—
56	#131×C₁₅₁	—	2	4	no	—
57	#131×C₁₅₁	—	2	4	no	—
58	#131×C₁₅₁	—	4	2	no	—
59	#131×C₁₅₁	—	4	2	no	—
60	C₂×M₁₆×C₁₅₁	—	2	2	no	—
61	C₂×M₁₆×C₁₅₁	—	2	2	no	—
62	C₂×M₁₆×C₁₅₁	C₂³	1	1	yes	characteristic
63	C₂×M₁₆×C₁₅₁	C₂³	1	2	yes	—
64	C₂×M₁₆×C₁₅₁	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₅₁	—	2	2	no	—
66	C₂²×C₈×C₁₅₁	—	2	2	no	—
67	C₂²×C₈×C₁₅₁	C₂³	1	2	yes	—
68	C₂²×C₈×C₁₅₁	C₂³	1	2	yes	—
69	C₄⋊Q₈×C₁₅₁	C₂×C₄	1	1	yes	characteristic
70	#127×C₁₅₁	C₂×C₄	1	1	yes	characteristic
71	#124×C₁₅₁	C₂×C₄	1	2	yes	—
72	#121×C₁₅₁	—	2	1	no	—
73	#121×C₁₅₁	—	2	1	no	—
74	C₄×Q₈×C₁₅₁	C₂×C₄	1	1	yes	characteristic
75	C₄×Q₈×C₁₅₁	C₂×C₄	1	1	yes	characteristic
76	C₄×D₄×C₁₅₁	—	2	1	no	—
77	C₄×D₄×C₁₅₁	—	2	1	no	—
78	C₄×D₄×C₁₅₁	—	2	1	no	—
79	C₄×D₄×C₁₅₁	—	2	1	no	—
80	C₄×D₄×C₁₅₁	C₂×C₄	1	1	yes	characteristic
81	C₄×D₄×C₁₅₁	C₂×C₄	1	1	yes	characteristic
82	#117×C₁₅₁	—	2	1	no	—
83	#117×C₁₅₁	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₁₅₁	—	2	1	no	—
85	C₂×C₄²×C₁₅₁	—	2	1	no	—
86	C₂×C₄²×C₁₅₁	—	2	1	no	—
87	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
90	#108×C₁₅₁	—	2	4	no	—
91	C₄⋊C₈×C₁₅₁	—	2	2	no	—
92	C₄⋊C₈×C₁₅₁	—	2	2	no	—
93	C₄⋊C₈×C₁₅₁	—	2	1	no	—
94	C₄⋊C₈×C₁₅₁	—	2	1	no	—
95	C₄⋊C₈×C₁₅₁	C₂×C₄	1	1	yes	characteristic
96	C₄⋊C₈×C₁₅₁	C₂×C₄	1	1	yes	characteristic
97	C₄⋊C₈×C₁₅₁	C₂×C₄	1	2	yes	—
98	C₄⋊C₈×C₁₅₁	D₄	1	1	yes	characteristic
99	C₄⋊C₈×C₁₅₁	D₄	1	1	yes	characteristic
100	C₄⋊C₈×C₁₅₁	D₄	1	2	yes	—
101	#104×C₁₅₁	—	2	4	no	—
102	#104×C₁₅₁	—	2	2	no	—
103	#104×C₁₅₁	—	4	2	no	—
104	#104×C₁₅₁	D₄	1	4	yes	complemented
105	#103×C₁₅₁	C₂×C₄	1	2	yes	—
106	#103×C₁₅₁	C₂×C₄	1	2	yes	—
107	#102×C₁₅₁	C₂×C₄	1	2	yes	—
108	#102×C₁₅₁	C₂×C₄	1	2	yes	—
109	C₂²⋊C₈×C₁₅₁	—	2	2	no	—
110	C₂²⋊C₈×C₁₅₁	—	2	2	no	—
111	#97×C₁₅₁	—	2	1	no	—
112	C₄×C₈×C₁₅₁	—	2	4	no	—
113	C₄×C₈×C₁₅₁	—	2	1	no	—
114	#41×C₁₅₁	—	2	1	no	—
115	#41×C₁₅₁	—	2	1	no	—
116	#41×C₁₅₁	—	2	2	no	—
117	#41×C₁₅₁	—	2	2	no	—
118	#41×C₁₅₁	—	2	2	no	—
119	#41×C₁₅₁	—	2	2	no	—
120	#41×C₁₅₁	C₂×D₄	1	2	yes	—
121	#41×C₁₅₁	#41	1	2	yes	—
122	C₂×Q₈×C₁₅₁	C₂²×C₄	1	2	yes	—
123	C₂×Q₈×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
124	C₂×D₄×C₁₅₁	—	2	1	no	—
125	C₂×D₄×C₁₅₁	—	2	2	no	—
126	C₂×D₄×C₁₅₁	—	2	1	no	—
127	C₂×D₄×C₁₅₁	—	2	1	no	—
128	C₂×D₄×C₁₅₁	C₂²×C₄	1	2	yes	—
129	C₂×D₄×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₅₁	—	2	1	no	—
131	C₂²×C₄×C₁₅₁	—	2	1	no	—
132	C₂²×C₄×C₁₅₁	—	2	1	no	—
133	C₂²×C₄×C₁₅₁	—	2	1	no	—
134	C₂²×C₄×C₁₅₁	—	2	2	no	—
135	C₂²×C₄×C₁₅₁	—	2	1	no	—
136	C₂²×C₄×C₁₅₁	#41	1	1	yes	characteristic
137	C₂²×C₄×C₁₅₁	#41	1	1	yes	characteristic
138	C₂²×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
139	Q₁₆×C₁₅₁	—	2	4	no	—
140	SD₁₆×C₁₅₁	—	2	4	no	—
141	SD₁₆×C₁₅₁	—	2	4	no	—
142	D₈×C₁₅₁	—	2	4	no	—
143	M₁₆×C₁₅₁	—	2	1	no	—
144	M₁₆×C₁₅₁	—	2	2	no	—
145	M₁₆×C₁₅₁	—	2	1	no	—
146	M₁₆×C₁₅₁	—	2	2	no	—
147	M₁₆×C₁₅₁	—	2	1	no	—
148	M₁₆×C₁₅₁	—	4	4	no	—
149	M₁₆×C₁₅₁	—	4	4	no	—
150	M₁₆×C₁₅₁	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₁₅₁	—	2	2	no	—
152	C₂×C₈×C₁₅₁	—	2	2	no	—
153	C₂×C₈×C₁₅₁	—	2	1	no	—
154	C₂×C₈×C₁₅₁	—	2	2	no	—
155	C₂×C₈×C₁₅₁	—	2	2	no	—
156	C₂×C₈×C₁₅₁	—	2	1	no	—
157	C₂×C₈×C₁₅₁	—	2	2	no	—
158	C₂×C₈×C₁₅₁	—	4	4	no	—
159	C₂×C₈×C₁₅₁	—	4	4	no	—
160	C₂×C₈×C₁₅₁	C₂²×C₄	1	2	yes	—
161	C₂×C₈×C₁₅₁	C₂²×C₄	1	2	yes	—
162	C₂×C₈×C₁₅₁	C₂×D₄	1	2	yes	—
163	C₂×C₈×C₁₅₁	C₂×D₄	1	2	yes	—
164	C₄⋊C₄×C₁₅₁	—	2	1	no	—
165	C₄⋊C₄×C₁₅₁	—	2	1	no	—
166	C₄⋊C₄×C₁₅₁	—	2	1	no	—
167	C₄⋊C₄×C₁₅₁	—	2	1	no	—
168	C₄⋊C₄×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
169	C₄⋊C₄×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
170	C₂²⋊C₄×C₁₅₁	—	2	1	no	—
171	C₂²⋊C₄×C₁₅₁	—	2	1	no	—
172	C₂²⋊C₄×C₁₅₁	—	2	1	no	—
173	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
174	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
175	C₄²×C₁₅₁	—	2	4	no	—
176	C₄²×C₁₅₁	—	2	1	no	—
177	C₄²×C₁₅₁	—	2	1	no	—
178	C₄²×C₁₅₁	—	2	1	no	—
179	C₄²×C₁₅₁	—	2	1	no	—
180	C₄²×C₁₅₁	—	2	1	no	—
181	C₄²×C₁₅₁	—	2	1	no	—
182	C₄²×C₁₅₁	—	4	2	no	—
183	C₄²×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
184	C₄²×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
185	C₄²×C₁₅₁	C₂×D₄	1	2	yes	—
186	C₄²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
188	C₂³×C₁₅₁	—	2	1	no	—
189	C₂³×C₁₅₁	—	2	2	no	—
190	C₂³×C₁₅₁	C₂×#41	1	1	yes	characteristic
191	Q₈×C₁₅₁	—	2	1	no	—
192	Q₈×C₁₅₁	—	2	2	no	—
193	Q₈×C₁₅₁	—	2	2	no	—
194	Q₈×C₁₅₁	C₄×D₄	1	2	yes	—
195	D₄×C₁₅₁	—	2	2	no	—
196	D₄×C₁₅₁	—	2	2	no	—
197	D₄×C₁₅₁	—	2	2	no	—
198	D₄×C₁₅₁	—	2	1	no	—
199	D₄×C₁₅₁	—	2	2	no	—
200	D₄×C₁₅₁	—	4	2	no	—
201	D₄×C₁₅₁	—	4	2	no	—
202	D₄×C₁₅₁	—	4	2	no	—
203	D₄×C₁₅₁	—	8	1	no	—
204	D₄×C₁₅₁	C₄×D₄	1	2	yes	—
205	C₂×C₄×C₁₅₁	—	2	2	no	—
206	C₂×C₄×C₁₅₁	—	2	2	no	—
207	C₂×C₄×C₁₅₁	—	2	1	no	—
208	C₂×C₄×C₁₅₁	—	2	2	no	—
209	C₂×C₄×C₁₅₁	—	2	2	no	—
210	C₂×C₄×C₁₅₁	—	2	2	no	—
211	C₂×C₄×C₁₅₁	—	2	2	no	—
212	C₂×C₄×C₁₅₁	—	2	2	no	—
213	C₂×C₄×C₁₅₁	—	2	2	no	—
214	C₂×C₄×C₁₅₁	—	2	1	no	—
215	C₂×C₄×C₁₅₁	—	2	1	no	—
216	C₂×C₄×C₁₅₁	—	4	1	no	—
217	C₂×C₄×C₁₅₁	—	4	1	no	—
218	C₂×C₄×C₁₅₁	—	4	1	no	—
219	C₂×C₄×C₁₅₁	—	4	2	no	—
220	C₂×C₄×C₁₅₁	—	4	2	no	—
221	C₂×C₄×C₁₅₁	—	4	2	no	—
222	C₂×C₄×C₁₅₁	—	8	1	no	—
223	C₂×C₄×C₁₅₁	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₅₁	C₄×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₅₁	C₄×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₅₁	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₅₁	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₁₅₁	H(5,𝔽₂)	1	1	yes	characteristic
232	C₂×C₄×C₁₅₁	2₋¹⁺⁴	1	1	yes	characteristic
233	C₈×C₁₅₁	—	2	2	no	—
234	C₈×C₁₅₁	—	2	2	no	—
235	C₈×C₁₅₁	—	2	2	no	—
236	C₈×C₁₅₁	—	2	2	no	—
237	C₈×C₁₅₁	—	2	2	no	—
238	C₈×C₁₅₁	—	4	2	no	—
239	C₈×C₁₅₁	—	4	1	no	—
240	C₂²×C₁₅₁	—	2	1	no	—
241	C₂²×C₁₅₁	—	2	1	no	—
242	C₂²×C₁₅₁	—	2	2	no	—
243	C₂²×C₁₅₁	—	4	1	no	—
244	C₂²×C₁₅₁	—	4	1	no	—
245	C₂²×C₁₅₁	—	4	2	no	—
246	C₂²×C₁₅₁	—	4	2	no	—
247	C₂²×C₁₅₁	—	4	2	no	—
248	C₂²×C₁₅₁	C₂×C₄×D₄	1	1	yes	characteristic
249	C₂²×C₁₅₁	#547	1	1	yes	characteristic
250	C₂²×C₁₅₁	#553	1	1	yes	characteristic
251	C₄×C₁₅₁	—	2	4	no	—
252	C₄×C₁₅₁	—	2	2	no	—
253	C₄×C₁₅₁	—	2	1	no	—
254	C₄×C₁₅₁	—	2	1	no	—
255	C₄×C₁₅₁	—	2	1	no	—
256	C₄×C₁₅₁	—	4	2	no	—
257	C₄×C₁₅₁	—	4	2	no	—
258	C₄×C₁₅₁	—	4	1	no	—
259	C₄×C₁₅₁	—	4	1	no	—
260	C₄×C₁₅₁	#443	1	2	yes	complemented
261	C₄×C₁₅₁	C₂×C₄×D₄	1	1	yes	characteristic
262	C₄×C₁₅₁	#520	1	1	yes	characteristic
263	C₄×C₁₅₁	D₄²	1	1	yes	characteristic
264	C₄×C₁₅₁	#548	1	1	yes	characteristic
265	C₂×C₁₅₁	—	2	1	no	—
266	C₂×C₁₅₁	—	2	1	no	—
267	C₂×C₁₅₁	—	4	2	no	—
268	C₂×C₁₅₁	—	8	2	no	—
269	C₂×C₁₅₁	#2361	1	1	yes	characteristic
270	C₂×C₁₅₁	C₂×#443	1	1	yes	characteristic
271	C₂×C₁₅₁	#2956	1	1	yes	characteristic
272	#23015	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
273	C₁₅₁	#23015	1	1	yes	characteristic, direct product factor, Sylow
274	#3035	C₂×C₁₅₁	1	1	yes	characteristic
275	C₂×#443	C₂×C₁₅₁	1	2	yes	complemented
276	#2935	C₂×C₁₅₁	1	1	yes	characteristic, complemented
277	#2906	C₂×C₁₅₁	1	1	yes	characteristic, complemented
278	#1962	C₂×C₁₅₁	1	1	yes	characteristic, complemented
279	#1950	C₂×C₁₅₁	1	1	yes	characteristic, complemented
280	#1937	C₂×C₁₅₁	1	2	yes	complemented
281	#1876	C₂×C₁₅₁	1	2	yes	complemented
282	#1866	C₂×C₁₅₁	1	2	yes	complemented
283	C₄×C₄⋊C₈	C₂×C₁₅₁	1	1	yes	characteristic, complemented
284	C₄×#104	C₂×C₁₅₁	1	1	yes	characteristic, complemented
285	C₂×#135	C₂²×C₁₅₁	1	2	yes	—
286	C₂×#131	C₂²×C₁₅₁	1	2	yes	—
287	C₂×#131	C₂²×C₁₅₁	1	2	yes	—
288	#532	C₂²×C₁₅₁	1	1	yes	characteristic
289	C₄×#41	C₂²×C₁₅₁	1	1	yes	characteristic
290	#464	C₄×C₁₅₁	1	2	yes	complemented
291	#463	C₄×C₁₅₁	1	2	yes	complemented
292	#462	C₄×C₁₅₁	1	1	yes	characteristic, complemented
293	#461	C₄×C₁₅₁	1	1	yes	characteristic, complemented
294	#460	C₄×C₁₅₁	1	1	yes	characteristic, complemented
295	#459	C₄×C₁₅₁	1	1	yes	characteristic, complemented
296	#443	—	2	8	no	—
297	#436	—	2	1	no	—
298	#435	—	2	2	no	—
299	C₈×D₄	—	2	1	no	—
300	C₂×#108	C₂²×C₁₅₁	1	2	yes	—
301	#424	—	2	2	no	—
302	#424	C₂²×C₁₅₁	1	2	yes	—
303	#423	—	2	1	no	—
304	#423	C₂²×C₁₅₁	1	1	yes	characteristic
305	C₂×C₄⋊C₈	—	2	1	no	—
306	C₂×C₄⋊C₈	C₂²×C₁₅₁	1	1	yes	characteristic
307	C₂×C₄⋊C₈	C₂²×C₁₅₁	1	1	yes	characteristic
308	C₂×#104	C₂²×C₁₅₁	1	1	yes	characteristic
309	C₂×#104	C₂²×C₁₅₁	1	2	yes	—
310	C₂×#104	C₂²×C₁₅₁	1	2	yes	—
311	C₂×#104	C₂²×C₁₅₁	1	1	yes	characteristic
312	#416	C₂²×C₁₅₁	1	2	yes	—
313	#408	C₂²×C₁₅₁	1	2	yes	—
314	C₄×M₁₆	C₂²×C₁₅₁	1	1	yes	characteristic
315	C₂×C₄×C₈	C₂²×C₁₅₁	1	2	yes	—
316	C₄³	C₂²×C₁₅₁	1	1	yes	characteristic
317	#341	C₂²×C₁₅₁	1	2	yes	—
318	#339	C₂²×C₁₅₁	1	1	yes	characteristic
319	#339	C₂²×C₁₅₁	1	1	yes	characteristic
320	#336	C₂²×C₁₅₁	1	2	yes	—
321	C₂×#41	C₂³×C₁₅₁	1	2	yes	—
322	C₂×#41	C₂³×C₁₅₁	1	1	yes	characteristic
323	#135	—	2	4	no	—
324	#135	—	2	4	no	—
325	C₂×Q₁₆	C₂×C₄×C₁₅₁	1	2	yes	—
326	C₂×SD₁₆	C₂×C₄×C₁₅₁	1	2	yes	—
327	C₂×SD₁₆	C₂×C₄×C₁₅₁	1	2	yes	—
328	C₂×D₈	C₂×C₄×C₁₅₁	1	2	yes	—
329	#131	—	2	4	no	—
330	#131	—	2	4	no	—
331	#131	—	4	2	no	—
332	#131	—	4	2	no	—
333	C₂×M₁₆	—	2	2	no	—
334	C₂×M₁₆	—	2	2	no	—
335	C₂×M₁₆	C₂³×C₁₅₁	1	2	yes	—
336	C₂×M₁₆	C₂³×C₁₅₁	1	1	yes	characteristic
337	C₂×M₁₆	C₂³×C₁₅₁	1	1	yes	characteristic
338	C₂²×C₈	—	2	2	no	—
339	C₂²×C₈	—	2	2	no	—
340	C₂²×C₈	C₂³×C₁₅₁	1	2	yes	—
341	C₂²×C₈	C₂³×C₁₅₁	1	2	yes	—
342	C₄⋊Q₈	C₂×C₄×C₁₅₁	1	1	yes	characteristic
343	#127	C₂×C₄×C₁₅₁	1	1	yes	characteristic
344	#124	C₂×C₄×C₁₅₁	1	2	yes	—
345	#121	—	2	1	no	—
346	#121	—	2	1	no	—
347	C₄×Q₈	C₂×C₄×C₁₅₁	1	1	yes	characteristic
348	C₄×Q₈	C₂×C₄×C₁₅₁	1	1	yes	characteristic
349	C₄×D₄	—	2	1	no	—
350	C₄×D₄	—	2	1	no	—
351	C₄×D₄	—	2	1	no	—
352	C₄×D₄	—	2	1	no	—
353	C₄×D₄	C₂×C₄×C₁₅₁	1	1	yes	characteristic
354	C₄×D₄	C₂×C₄×C₁₅₁	1	1	yes	characteristic
355	#117	—	2	1	no	—
356	#117	C₂³×C₁₅₁	1	1	yes	characteristic
357	C₂×C₄²	—	2	1	no	—
358	C₂×C₄²	—	2	1	no	—
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
361	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
362	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
363	#108	—	2	4	no	—
364	C₄⋊C₈	—	2	2	no	—
365	C₄⋊C₈	—	2	2	no	—
366	C₄⋊C₈	—	2	1	no	—
367	C₄⋊C₈	—	2	1	no	—
368	C₄⋊C₈	C₂×C₄×C₁₅₁	1	1	yes	characteristic
369	C₄⋊C₈	C₂×C₄×C₁₅₁	1	1	yes	characteristic
370	C₄⋊C₈	C₂×C₄×C₁₅₁	1	2	yes	—
371	C₄⋊C₈	D₄×C₁₅₁	1	1	yes	characteristic
372	C₄⋊C₈	D₄×C₁₅₁	1	1	yes	characteristic
373	C₄⋊C₈	D₄×C₁₅₁	1	2	yes	—
374	#104	—	2	2	no	—
375	#104	—	2	4	no	—
376	#104	—	4	2	no	—
377	#104	D₄×C₁₅₁	1	4	yes	complemented
378	#103	C₂×C₄×C₁₅₁	1	2	yes	—
379	#103	C₂×C₄×C₁₅₁	1	2	yes	—
380	#102	C₂×C₄×C₁₅₁	1	2	yes	—
381	#102	C₂×C₄×C₁₅₁	1	2	yes	—
382	C₂²⋊C₈	—	2	2	no	—
383	C₂²⋊C₈	—	2	2	no	—
384	#97	—	2	1	no	—
385	C₄×C₈	—	2	4	no	—
386	C₄×C₈	—	2	1	no	—
387	#41	—	2	1	no	—
388	#41	—	2	1	no	—
389	#41	—	2	2	no	—
390	#41	—	2	2	no	—
391	#41	—	2	2	no	—
392	#41	—	2	2	no	—
393	#41	C₂×D₄×C₁₅₁	1	2	yes	—
394	#41	#41×C₁₅₁	1	2	yes	—
395	C₂×Q₈	C₂²×C₄×C₁₅₁	1	2	yes	—
396	C₂×Q₈	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	C₂²×C₄×C₁₅₁	1	2	yes	—
402	C₂×D₄	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	#41×C₁₅₁	1	1	yes	characteristic
410	C₂²×C₄	#41×C₁₅₁	1	1	yes	characteristic
411	C₂²×C₄	C₂⁴×C₁₅₁	1	1	yes	characteristic
412	Q₁₆	—	2	4	no	—
413	SD₁₆	—	2	4	no	—
414	SD₁₆	—	2	4	no	—
415	D₈	—	2	4	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	2	2	no	—
418	M₁₆	—	2	1	no	—
419	M₁₆	—	2	2	no	—
420	M₁₆	—	2	1	no	—
421	M₁₆	—	4	4	no	—
422	M₁₆	—	4	4	no	—
423	M₁₆	C₂×D₄×C₁₅₁	1	2	yes	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	4	4	no	—
432	C₂×C₈	—	4	4	no	—
433	C₂×C₈	C₂²×C₄×C₁₅₁	1	2	yes	—
434	C₂×C₈	C₂²×C₄×C₁₅₁	1	2	yes	—
435	C₂×C₈	C₂×D₄×C₁₅₁	1	2	yes	—
436	C₂×C₈	C₂×D₄×C₁₅₁	1	2	yes	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
442	C₄⋊C₄	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
443	C₂²⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	2	1	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₄²	—	2	4	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	2	1	no	—
455	C₄²	—	4	2	no	—
456	C₄²	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
457	C₄²	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
458	C₄²	C₂×D₄×C₁₅₁	1	2	yes	—
459	C₄²	C₂×D₄×C₁₅₁	1	1	yes	characteristic
460	C₄²	C₂×D₄×C₁₅₁	1	1	yes	characteristic
461	C₂³	—	2	1	no	—
462	C₂³	—	2	2	no	—
463	C₂³	C₂×#41×C₁₅₁	1	1	yes	characteristic
464	Q₈	—	2	1	no	—
465	Q₈	—	2	2	no	—
466	Q₈	—	2	2	no	—
467	Q₈	C₄×D₄×C₁₅₁	1	2	yes	—
468	D₄	—	2	2	no	—
469	D₄	—	2	2	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	1	no	—
472	D₄	—	2	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	8	1	no	—
477	D₄	C₄×D₄×C₁₅₁	1	2	yes	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	8	1	no	—
496	C₂×C₄	C₄×D₄×C₁₅₁	1	1	yes	characteristic
497	C₂×C₄	C₄×D₄×C₁₅₁	1	1	yes	characteristic
498	C₂×C₄	C₄×D₄×C₁₅₁	1	1	yes	characteristic
499	C₂×C₄	C₄×D₄×C₁₅₁	1	1	yes	characteristic
500	C₂×C₄	C₂³×C₄×C₁₅₁	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
502	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
503	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
504	C₂×C₄	H(5,𝔽₂)×C₁₅₁	1	1	yes	characteristic
505	C₂×C₄	2₋¹⁺⁴×C₁₅₁	1	1	yes	characteristic
506	C₈	—	2	2	no	—
507	C₈	—	2	2	no	—
508	C₈	—	2	2	no	—
509	C₈	—	2	2	no	—
510	C₈	—	2	2	no	—
511	C₈	—	4	2	no	—
512	C₈	—	4	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	C₂×C₄×D₄×C₁₅₁	1	1	yes	characteristic
522	C₂²	#547×C₁₅₁	1	1	yes	characteristic
523	C₂²	#553×C₁₅₁	1	1	yes	characteristic
524	C₄	—	2	4	no	—
525	C₄	—	2	2	no	—
526	C₄	—	2	1	no	—
527	C₄	—	2	1	no	—
528	C₄	—	2	1	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	2	no	—
531	C₄	—	4	1	no	—
532	C₄	—	4	1	no	—
533	C₄	#443×C₁₅₁	1	2	yes	complemented
534	C₄	C₂×C₄×D₄×C₁₅₁	1	1	yes	characteristic
535	C₄	#520×C₁₅₁	1	1	yes	characteristic
536	C₄	D₄²×C₁₅₁	1	1	yes	characteristic
537	C₄	#548×C₁₅₁	1	1	yes	characteristic
538	C₂	—	2	1	no	—
539	C₂	—	2	1	no	—
540	C₂	—	4	2	no	—
541	C₂	—	8	2	no	—
542	C₂	#2361×C₁₅₁	1	1	yes	characteristic
543	C₂	C₂×#443×C₁₅₁	1	1	yes	characteristic
544	C₂	#2956×C₁₅₁	1	1	yes	characteristic

	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	#3035×C₁₅₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₅₁ ◁ C₂×C₄⋊C₈×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. #2935×C₁₅₁	C₂	semidirect
4. #2906×C₁₅₁	C₂	semidirect
5. #1962×C₁₅₁	C₂	semidirect
6. #1950×C₁₅₁	C₂	semidirect
7. #1937×C₁₅₁	C₂	semidirect
8. #1876×C₁₅₁	C₂	semidirect
9. #1866×C₁₅₁	C₂	semidirect
10. C₄×C₄⋊C₈×C₁₅₁	C₂	semidirect
11. C₄×#104×C₁₅₁	C₂	semidirect
17. #464×C₁₅₁	C₄	semidirect
18. #463×C₁₅₁	C₄	semidirect
19. #462×C₁₅₁	C₄	semidirect
20. #461×C₁₅₁	C₄	semidirect
21. #460×C₁₅₁	C₄	semidirect
22. #459×C₁₅₁	C₄	semidirect
104. #104×C₁₅₁	D₄	semidirect
260. C₄×C₁₅₁	#443	semidirect
272. #23015	C₁₅₁	direct (N × H)
273. C₁₅₁	#23015	direct (N × H)
275. C₂×#443	C₂×C₁₅₁	semidirect
276. #2935	C₂×C₁₅₁	semidirect
277. #2906	C₂×C₁₅₁	semidirect
278. #1962	C₂×C₁₅₁	semidirect
279. #1950	C₂×C₁₅₁	semidirect
280. #1937	C₂×C₁₅₁	semidirect
281. #1876	C₂×C₁₅₁	semidirect
282. #1866	C₂×C₁₅₁	semidirect
283. C₄×C₄⋊C₈	C₂×C₁₅₁	semidirect
284. C₄×#104	C₂×C₁₅₁	semidirect
290. #464	C₄×C₁₅₁	semidirect
291. #463	C₄×C₁₅₁	semidirect
292. #462	C₄×C₁₅₁	semidirect
293. #461	C₄×C₁₅₁	semidirect
294. #460	C₄×C₁₅₁	semidirect
295. #459	C₄×C₁₅₁	semidirect
377. #104	D₄×C₁₅₁	semidirect
533. C₄	#443×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
#3035×C₁₅₁	2
C₂×#443×C₁₅₁	2
#2935×C₁₅₁	2
#2906×C₁₅₁	2
#1962×C₁₅₁	2
#1950×C₁₅₁	2
#1937×C₁₅₁	2
#1876×C₁₅₁	2
#1866×C₁₅₁	2
C₄×C₄⋊C₈×C₁₅₁	2
C₄×#104×C₁₅₁	2
#23015	151

Subgroups — C151×#23015 #50327940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#23015 #50327940